Bessel_function.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Bessel_function.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOKo+q/9zlMZvMwC58EtmzC",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "d1e107d52a21498fadea284fa6923d66": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "VBoxModel",
          "state": {
            "_view_name": "VBoxView",
            "_dom_classes": [
              "widget-interact"
            ],
            "_model_name": "VBoxModel",
            "_view_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ef0644985e5f420186b72827c8b45487",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1c34112811cf40c6b25d350d6339a781",
              "IPY_MODEL_a7497ed2202c4f71a3038ca14dce5a9f",
              "IPY_MODEL_42d210a862ad4618946c2b6adc56c35f"
            ]
          }
        },
        "ef0644985e5f420186b72827c8b45487": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1c34112811cf40c6b25d350d6339a781": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SelectMultipleModel",
          "state": {
            "_options_labels": [
              "0",
              "1",
              "2",
              "3",
              "4",
              "5"
            ],
            "_view_name": "SelectMultipleView",
            "style": "IPY_MODEL_89abfec08149443cb3507dc20de35d15",
            "rows": 5,
            "_dom_classes": [],
            "description": "Bessel Order",
            "_model_name": "SelectMultipleModel",
            "index": [
              0
            ],
            "_view_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "disabled": false,
            "_view_module_version": "1.5.0",
            "description_tooltip": null,
            "_model_module": "@jupyter-widgets/controls",
            "layout": "IPY_MODEL_98fa4f19090342a8b42152ad2bfa5390"
          }
        },
        "a7497ed2202c4f71a3038ca14dce5a9f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "state": {
            "_view_name": "FloatSliderView",
            "style": "IPY_MODEL_4e9ba8db56a948fa96f5681739287dc1",
            "_dom_classes": [],
            "description": "Freq",
            "step": 0.1,
            "_model_name": "FloatSliderModel",
            "orientation": "horizontal",
            "max": 20,
            "_view_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "value": 1,
            "_view_count": null,
            "disabled": false,
            "_view_module_version": "1.5.0",
            "min": 1,
            "continuous_update": true,
            "readout_format": ".2f",
            "description_tooltip": null,
            "readout": true,
            "_model_module": "@jupyter-widgets/controls",
            "layout": "IPY_MODEL_7dc19eb7edd54b68bcda4235ac8ada9d"
          }
        },
        "42d210a862ad4618946c2b6adc56c35f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [
              {
                "output_type": "display_data",
                "metadata": {
                  "tags": []
                },
                "text/html": "<div>\n        \n        \n            <div id=\"73ce9277-97c9-4bbf-9406-3e8a2537eca8\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n            <script type=\"text/javascript\">\n                require([\"plotly\"], function(Plotly) {\n                    window.PLOTLYENV=window.PLOTLYENV || {};\n                    \n                if (document.getElementById(\"73ce9277-97c9-4bbf-9406-3e8a2537eca8\")) {\n                    Plotly.newPlot(\n                        '73ce9277-97c9-4bbf-9406-3e8a2537eca8',\n                        [{\"line\": {\"shape\": \"spline\"}, \"mode\": \"lines\", \"name\": \"Bessel0\", \"type\": \"scatter\", \"x\": [0.0, 0.010506998841437435, 0.02101399768287487, 0.031520996524312304, 0.04202799536574974, 0.05253499420718718, 0.06304199304862461, 0.07354899189006205, 0.08405599073149948, 0.09456298957293692, 0.10506998841437436, 0.1155769872558118, 0.12608398609724922, 0.13659098493868665, 0.1470979837801241, 0.15760498262156153, 0.16811198146299897, 0.1786189803044364, 0.18912597914587384, 0.19963297798731128, 0.21013997682874871, 0.22064697567018615, 0.2311539745116236, 0.24166097335306103, 0.25216797219449844, 0.2626749710359359, 0.2731819698773733, 0.2836889687188108, 0.2941959675602482, 0.30470296640168565, 0.31520996524312306, 0.3257169640845605, 0.33622396292599793, 0.34673096176743534, 0.3572379606088728, 0.3677449594503102, 0.3782519582917477, 0.3887589571331851, 0.39926595597462256, 0.40977295481605996, 0.42027995365749743, 0.43078695249893484, 0.4412939513403723, 0.4518009501818097, 0.4623079490232472, 0.4728149478646846, 0.48332194670612205, 0.49382894554755946, 0.5043359443889969, 0.5148429432304343, 0.5253499420718718, 0.5358569409133092, 0.5463639397547466, 0.5568709385961841, 0.5673779374376215, 0.5778849362790589, 0.5883919351204964, 0.5988989339619338, 0.6094059328033713, 0.6199129316448087, 0.6304199304862461, 0.6409269293276836, 0.651433928169121, 0.6619409270105584, 0.6724479258519959, 0.6829549246934333, 0.6934619235348707, 0.7039689223763081, 0.7144759212177456, 0.7249829200591831, 0.7354899189006204, 0.7459969177420579, 0.7565039165834954, 0.7670109154249328, 0.7775179142663702, 0.7880249131078076, 0.7985319119492451, 0.8090389107906826, 0.8195459096321199, 0.8300529084735574, 0.8405599073149949, 0.8510669061564322, 0.8615739049978697, 0.8720809038393071, 0.8825879026807446, 0.893094901522182, 0.9036019003636194, 0.9141088992050569, 0.9246158980464944, 0.9351228968879317, 0.9456298957293692, 0.9561368945708066, 0.9666438934122441, 0.9771508922536815, 0.9876578910951189, 0.9981648899365564, 1.0086718887779937, 1.0191788876194312, 1.0296858864608687, 1.0401928853023061, 1.0506998841437436, 1.061206882985181, 1.0717138818266183, 1.0822208806680558, 1.0927278795094932, 1.1032348783509307, 1.1137418771923682, 1.1242488760338056, 1.134755874875243, 1.1452628737166806, 1.1557698725581178, 1.1662768713995553, 1.1767838702409927, 1.1872908690824302, 1.1977978679238677, 1.2083048667653051, 1.2188118656067426, 1.2293188644481798, 1.2398258632896173, 1.2503328621310548, 1.2608398609724922, 1.2713468598139297, 1.2818538586553672, 1.2923608574968046, 1.302867856338242, 1.3133748551796793, 1.3238818540211168, 1.3343888528625543, 1.3448958517039917, 1.3554028505454292, 1.3659098493868667, 1.3764168482283041, 1.3869238470697414, 1.3974308459111788, 1.4079378447526163, 1.4184448435940538, 1.4289518424354912, 1.4394588412769287, 1.4499658401183662, 1.4604728389598036, 1.4709798378012409, 1.4814868366426783, 1.4919938354841158, 1.5025008343255533, 1.5130078331669907, 1.5235148320084282, 1.5340218308498657, 1.544528829691303, 1.5550358285327404, 1.5655428273741778, 1.5760498262156153, 1.5865568250570528, 1.5970638238984902, 1.6075708227399277, 1.6180778215813651, 1.6285848204228024, 1.6390918192642399, 1.6495988181056773, 1.6601058169471148, 1.6706128157885523, 1.6811198146299897, 1.6916268134714272, 1.7021338123128644, 1.712640811154302, 1.7231478099957394, 1.7336548088371768, 1.7441618076786143, 1.7546688065200517, 1.7651758053614892, 1.7756828042029267, 1.786189803044364, 1.7966968018858014, 1.8072038007272389, 1.8177107995686763, 1.8282177984101138, 1.8387247972515512, 1.8492317960929887, 1.859738794934426, 1.8702457937758634, 1.8807527926173009, 1.8912597914587383, 1.9017667903001758, 1.9122737891416133, 1.9227807879830507, 1.9332877868244882, 1.9437947856659255, 1.954301784507363, 1.9648087833488004, 1.9753157821902378, 1.9858227810316753, 1.9963297798731128, 2.00683677871455, 2.0173437775559875, 2.027850776397425, 2.0383577752388624, 2.0488647740803, 2.0593717729217373, 2.069878771763175, 2.0803857706046123, 2.0908927694460497, 2.101399768287487, 2.1119067671289247, 2.122413765970362, 2.1329207648117996, 2.1434277636532366, 2.153934762494674, 2.1644417613361115, 2.174948760177549, 2.1854557590189865, 2.195962757860424, 2.2064697567018614, 2.216976755543299, 2.2274837543847363, 2.237990753226174, 2.2484977520676113, 2.2590047509090487, 2.269511749750486, 2.2800187485919237, 2.290525747433361, 2.301032746274798, 2.3115397451162356, 2.322046743957673, 2.3325537427991105, 2.343060741640548, 2.3535677404819855, 2.364074739323423, 2.3745817381648604, 2.385088737006298, 2.3955957358477353, 2.406102734689173, 2.4166097335306103, 2.4271167323720477, 2.437623731213485, 2.4481307300549227, 2.4586377288963597, 2.469144727737797, 2.4796517265792346, 2.490158725420672, 2.5006657242621095, 2.511172723103547, 2.5216797219449845, 2.532186720786422, 2.5426937196278594, 2.553200718469297, 2.5637077173107343, 2.574214716152172, 2.5847217149936093, 2.5952287138350467, 2.605735712676484, 2.616242711517921, 2.6267497103593587, 2.637256709200796, 2.6477637080422336, 2.658270706883671, 2.6687777057251085, 2.679284704566546, 2.6897917034079835, 2.700298702249421, 2.7108057010908584, 2.721312699932296, 2.7318196987737333, 2.742326697615171, 2.7528336964566082, 2.7633406952980457, 2.7738476941394827, 2.78435469298092, 2.7948616918223577, 2.805368690663795, 2.8158756895052326, 2.82638268834667, 2.8368896871881075, 2.847396686029545, 2.8579036848709825, 2.86841068371242, 2.8789176825538574, 2.889424681395295, 2.8999316802367323, 2.9104386790781698, 2.9209456779196072, 2.9314526767610443, 2.9419596756024817, 2.952466674443919, 2.9629736732853567, 2.973480672126794, 2.9839876709682316, 2.994494669809669, 3.0050016686511065, 3.015508667492544, 3.0260156663339814, 3.036522665175419, 3.0470296640168564, 3.057536662858294, 3.0680436616997313, 3.0785506605411688, 3.089057659382606, 3.0995646582240433, 3.1100716570654807, 3.120578655906918, 3.1310856547483557, 3.141592653589793], \"y\": [1.0, 0.9999724009342658, 0.9998896060221844, 0.9997516221189114, 0.9995584606490046, 0.9993101376053732, 0.999006673547807, 0.9986480936010855, 0.9982344274526649, 0.9977657093499482, 0.9972419780971347, 0.9966632770516501, 0.9960296541201578, 0.9953411617541525, 0.9945978569451351, 0.9937998012193701, 0.9929470606322266, 0.9920397057621018, 0.9910778117039298, 0.990061458062275, 0.9889907289440082, 0.9878657129505742, 0.9866865031698411, 0.9854531971675395, 0.9841658969782908, 0.9828247090962231, 0.9814297444651787, 0.9799811184685124, 0.9784789509184818, 0.976923366045231, 0.9753144924853682, 0.9736524632701392, 0.9719374158131978, 0.9701694918979717, 0.9683488376646305, 0.9664756035966517, 0.9645499445069882, 0.9625720195238398, 0.9605419920760276, 0.9584600298779754, 0.9563263049142972, 0.954140993423992, 0.9519042758842523, 0.9496163369938798, 0.9472773656563177, 0.9448875549622963, 0.9424471021720957, 0.9399562086974254, 0.9374150800829262, 0.9348239259872921, 0.9321829601640166, 0.9294924004417638, 0.926752468704367, 0.9239633908704581, 0.9211253968727257, 0.9182387206368078, 0.9153036000598201, 0.9123202769885216, 0.9092889971971185, 0.9062100103647104, 0.9030835700523813, 0.8999099336799351, 0.8966893625022795, 0.8934221215854617, 0.8901084797823551, 0.8867487097080029, 0.8833430877146173, 0.8798918938662412, 0.8763954119130692, 0.8728539292654367, 0.8692677369674738, 0.8656371296704297, 0.8619624056056717, 0.8582438665573556, 0.8544818178347771, 0.8506765682444014, 0.8468284300615774, 0.8429377190019371, 0.8390047541924829, 0.8350298581423671, 0.8310133567133657, 0.8269555790900478, 0.8228568577496475, 0.8187175284316353, 0.8145379301069983, 0.8103184049472266, 0.8060592982930129, 0.8017609586226659, 0.7974237375202423, 0.7930479896433991, 0.7886340726909682, 0.7841823473702618, 0.7796931773641043, 0.7751669292975983, 0.770603972704629, 0.766004679994106, 0.7613694264159498, 0.7566985900268224, 0.7519925516556104, 0.7472516948686587, 0.7424764059347609, 0.7376670737899093, 0.7328240900018087, 0.7279478487341553, 0.7230387467106859, 0.7180971831790012, 0.7131235598741635, 0.7081182809820786, 0.7030817531026557, 0.6980143852127615, 0.6929165886289584, 0.6877887769700427, 0.6826313661193762, 0.6774447741870241, 0.6722294214716934, 0.6669857304224834, 0.6617141256004487, 0.6564150336399759, 0.6510888832099837, 0.6457361049749447, 0.6403571315557339, 0.634952397490311, 0.6295223391942355, 0.624067394921021, 0.6185880047223328, 0.6130846104080321, 0.6075576555060668, 0.6020075852222238, 0.5964348463997298, 0.5908398874787224, 0.5852231584555816, 0.5795851108421323, 0.5739261976247207, 0.5682468732231682, 0.5625475934496054, 0.5568288154671919, 0.5510909977487269, 0.54533460003515, 0.5395600832939422, 0.533767909677424, 0.5279585424809644, 0.5221324461010929, 0.5162900859935281, 0.5104319286311235, 0.5045584414617329, 0.49867009286600084, 0.4927673521150844, 0.4868506893283064, 0.48092057543074473, 0.47497748211076685, 0.46902188177750564, 0.46305424751828705, 0.45707505305601, 0.45108477270648445, 0.44508388133573173, 0.4390728543172485, 0.43305216748924247, 0.4270222971118412, 0.42098371982427885, 0.4149369126020641, 0.40888235271413675, 0.4028205176800103, 0.3967518852269131, 0.3906769332469244, 0.38459613975411505, 0.37850998284169385, 0.37241894063916325, 0.3663234912694923, 0.3602241128063059, 0.35412128323109776, 0.3480154803904702, 0.3419071819534043, 0.3357968653685666, 0.32968500782165205, 0.3235720861927725, 0.317458577013891, 0.31134495642630755, 0.30523170013819984, 0.2991192833822229, 0.2930081808731737, 0.2868988667657198, 0.280791814612202, 0.27468749732051106, 0.26858638711204313, 0.2624889554797399, 0.2563956731462135, 0.25030701002196504, 0.24422343516369693, 0.23814541673272357, 0.23207342195348632, 0.22600791707217407, 0.21994936731545603, 0.21389823684932668, 0.20785498873807268, 0.2018200849033586, 0.1957939860834417, 0.18977715179251467, 0.1837700402801843, 0.17777310849108552, 0.1717868120246392, 0.16581160509495452, 0.15984794049087891, 0.1538962695362037, 0.1479570420500232, 0.14203070630725734, 0.13611770899933476, 0.1302184951950469, 0.12433350830157139, 0.11846319002567147, 0.11260798033507277, 0.10676831742002434, 0.1009446376550432, 0.0951373755608516, 0.08934696376650243, 0.08357383297170672, 0.0778184119093568, 0.07208112730825546, 0.0663624038560515, 0.060662664162384874, 0.054982328722248314, 0.049321815879561706, 0.04368154179097365, 0.03806192038988065, 0.03246336335067897, 0.026886280053242482, 0.021331077547639066, 0.01579816051908176, 0.010287931253121309, 0.00480078960108143, -0.0006628670542562377, -0.00610264383272041, -0.011518148390562439, -0.016908990954013155, -0.02227478435258021, -0.027615144052081955, -0.03292968818741779, -0.03821803759506612, -0.04347981584531405, -0.04871464927421088, -0.05392216701524391, -0.059102001030734076, -0.06425378614294777, -0.06937716006492368, -0.0744717634310085, -0.07953723982710151, -0.08457323582060713, -0.08957940099008532, -0.0945553879546049, -0.09950085240279521, -0.10441545312158886, -0.10929885202465889, -0.11415071418054586, -0.11897070784046955, -0.12375850446582674, -0.12851377875536996, -0.13323620867206598, -0.1379254754696325, -0.14258126371874613, -0.14720326133292627, -0.15179115959408562, -0.1563446531777521, -0.1608634401779522, -0.16534722213175898, -0.16979570404350305, -0.1742085944086374, -0.1785856052372652, -0.18292645207731634, -0.18723085403738016, -0.1914985338091859, -0.19572921768973583, -0.19992263560307935, -0.2040785211217362, -0.20819661148776006, -0.2122766476334446, -0.21631837420166633, -0.2203215395658675, -0.2242858958496724, -0.22821119894613873, -0.2320972085366404, -0.23594368810938146, -0.23975040497753936, -0.24351713029703415, -0.24724363908392508, -0.2509297102314311, -0.2545751265265749, -0.2581796746664452, -0.2617431452740866, -0.2652653329140002, -0.268746036107266, -0.2721850573462823, -0.27558220310911713, -0.2789372838734767, -0.28225011413028456, -0.2855205123968735, -0.28874830122978795, -0.29193330723719607, -0.29507536109090926, -0.2981742975380115, -0.3012299554120938, -0.3042421776440939]}],\n                        {\"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"<b>ILLUSTRATION</b>\"}, \"xaxis\": {\"title\": {\"text\": \"<i> (nanoseconds)</i>\"}}, \"yaxis\": {\"title\": {\"text\": \"<i>(nanoseconds),/i>\"}}},\n                        {\"responsive\": true}\n                    ).then(function(){\n                            \nvar gd = document.getElementById('73ce9277-97c9-4bbf-9406-3e8a2537eca8');\nvar x = new MutationObserver(function (mutations, observer) {{\n        var display = window.getComputedStyle(gd).display;\n        if (!display || display === 'none') {{\n            console.log([gd, 'removed!']);\n            Plotly.purge(gd);\n            observer.disconnect();\n        }}\n}});\n\n// Listen for the removal of the full notebook cells\nvar notebookContainer = gd.closest('#notebook-container');\nif (notebookContainer) {{\n    x.observe(notebookContainer, {childList: true});\n}}\n\n// Listen for the clearing of the current output cell\nvar outputEl = gd.closest('.output');\nif (outputEl) {{\n    x.observe(outputEl, {childList: true});\n}}\n\n                        })\n                };\n                });\n            </script>\n        </div>",
                "application/vnd.plotly.v1+json": {
                  "data": [
                    {
                      "name": "Bessel0",
                      "mode": "lines",
                      "y": [
                        1,
                        0.9999724009342658,
                        0.9998896060221844,
                        0.9997516221189114,
                        0.9995584606490046,
                        0.9993101376053732,
                        0.999006673547807,
                        0.9986480936010855,
                        0.9982344274526649,
                        0.9977657093499482,
                        0.9972419780971347,
                        0.9966632770516501,
                        0.9960296541201578,
                        0.9953411617541525,
                        0.9945978569451351,
                        0.9937998012193701,
                        0.9929470606322266,
                        0.9920397057621018,
                        0.9910778117039298,
                        0.990061458062275,
                        0.9889907289440082,
                        0.9878657129505742,
                        0.9866865031698411,
                        0.9854531971675395,
                        0.9841658969782908,
                        0.9828247090962231,
                        0.9814297444651787,
                        0.9799811184685124,
                        0.9784789509184818,
                        0.976923366045231,
                        0.9753144924853682,
                        0.9736524632701392,
                        0.9719374158131978,
                        0.9701694918979717,
                        0.9683488376646305,
                        0.9664756035966517,
                        0.9645499445069882,
                        0.9625720195238398,
                        0.9605419920760276,
                        0.9584600298779754,
                        0.9563263049142972,
                        0.954140993423992,
                        0.9519042758842523,
                        0.9496163369938798,
                        0.9472773656563177,
                        0.9448875549622963,
                        0.9424471021720957,
                        0.9399562086974254,
                        0.9374150800829262,
                        0.9348239259872921,
                        0.9321829601640166,
                        0.9294924004417638,
                        0.926752468704367,
                        0.9239633908704581,
                        0.9211253968727257,
                        0.9182387206368078,
                        0.9153036000598201,
                        0.9123202769885216,
                        0.9092889971971185,
                        0.9062100103647104,
                        0.9030835700523813,
                        0.8999099336799351,
                        0.8966893625022795,
                        0.8934221215854617,
                        0.8901084797823551,
                        0.8867487097080029,
                        0.8833430877146173,
                        0.8798918938662412,
                        0.8763954119130692,
                        0.8728539292654367,
                        0.8692677369674738,
                        0.8656371296704297,
                        0.8619624056056717,
                        0.8582438665573556,
                        0.8544818178347771,
                        0.8506765682444014,
                        0.8468284300615774,
                        0.8429377190019371,
                        0.8390047541924829,
                        0.8350298581423671,
                        0.8310133567133657,
                        0.8269555790900478,
                        0.8228568577496475,
                        0.8187175284316353,
                        0.8145379301069983,
                        0.8103184049472266,
                        0.8060592982930129,
                        0.8017609586226659,
                        0.7974237375202423,
                        0.7930479896433991,
                        0.7886340726909682,
                        0.7841823473702618,
                        0.7796931773641043,
                        0.7751669292975983,
                        0.770603972704629,
                        0.766004679994106,
                        0.7613694264159498,
                        0.7566985900268224,
                        0.7519925516556104,
                        0.7472516948686587,
                        0.7424764059347609,
                        0.7376670737899093,
                        0.7328240900018087,
                        0.7279478487341553,
                        0.7230387467106859,
                        0.7180971831790012,
                        0.7131235598741635,
                        0.7081182809820786,
                        0.7030817531026557,
                        0.6980143852127615,
                        0.6929165886289584,
                        0.6877887769700427,
                        0.6826313661193762,
                        0.6774447741870241,
                        0.6722294214716934,
                        0.6669857304224834,
                        0.6617141256004487,
                        0.6564150336399759,
                        0.6510888832099837,
                        0.6457361049749447,
                        0.6403571315557339,
                        0.634952397490311,
                        0.6295223391942355,
                        0.624067394921021,
                        0.6185880047223328,
                        0.6130846104080321,
                        0.6075576555060668,
                        0.6020075852222238,
                        0.5964348463997298,
                        0.5908398874787224,
                        0.5852231584555816,
                        0.5795851108421323,
                        0.5739261976247207,
                        0.5682468732231682,
                        0.5625475934496054,
                        0.5568288154671919,
                        0.5510909977487269,
                        0.54533460003515,
                        0.5395600832939422,
                        0.533767909677424,
                        0.5279585424809644,
                        0.5221324461010929,
                        0.5162900859935281,
                        0.5104319286311235,
                        0.5045584414617329,
                        0.49867009286600084,
                        0.4927673521150844,
                        0.4868506893283064,
                        0.48092057543074473,
                        0.47497748211076685,
                        0.46902188177750564,
                        0.46305424751828705,
                        0.45707505305601,
                        0.45108477270648445,
                        0.44508388133573173,
                        0.4390728543172485,
                        0.43305216748924247,
                        0.4270222971118412,
                        0.42098371982427885,
                        0.4149369126020641,
                        0.40888235271413675,
                        0.4028205176800103,
                        0.3967518852269131,
                        0.3906769332469244,
                        0.38459613975411505,
                        0.37850998284169385,
                        0.37241894063916325,
                        0.3663234912694923,
                        0.3602241128063059,
                        0.35412128323109776,
                        0.3480154803904702,
                        0.3419071819534043,
                        0.3357968653685666,
                        0.32968500782165205,
                        0.3235720861927725,
                        0.317458577013891,
                        0.31134495642630755,
                        0.30523170013819984,
                        0.2991192833822229,
                        0.2930081808731737,
                        0.2868988667657198,
                        0.280791814612202,
                        0.27468749732051106,
                        0.26858638711204313,
                        0.2624889554797399,
                        0.2563956731462135,
                        0.25030701002196504,
                        0.24422343516369693,
                        0.23814541673272357,
                        0.23207342195348632,
                        0.22600791707217407,
                        0.21994936731545603,
                        0.21389823684932668,
                        0.20785498873807268,
                        0.2018200849033586,
                        0.1957939860834417,
                        0.18977715179251467,
                        0.1837700402801843,
                        0.17777310849108552,
                        0.1717868120246392,
                        0.16581160509495452,
                        0.15984794049087891,
                        0.1538962695362037,
                        0.1479570420500232,
                        0.14203070630725734,
                        0.13611770899933476,
                        0.1302184951950469,
                        0.12433350830157139,
                        0.11846319002567147,
                        0.11260798033507277,
                        0.10676831742002434,
                        0.1009446376550432,
                        0.0951373755608516,
                        0.08934696376650243,
                        0.08357383297170672,
                        0.0778184119093568,
                        0.07208112730825546,
                        0.0663624038560515,
                        0.060662664162384874,
                        0.054982328722248314,
                        0.049321815879561706,
                        0.04368154179097365,
                        0.03806192038988065,
                        0.03246336335067897,
                        0.026886280053242482,
                        0.021331077547639066,
                        0.01579816051908176,
                        0.010287931253121309,
                        0.00480078960108143,
                        -0.0006628670542562377,
                        -0.00610264383272041,
                        -0.011518148390562439,
                        -0.016908990954013155,
                        -0.02227478435258021,
                        -0.027615144052081955,
                        -0.03292968818741779,
                        -0.03821803759506612,
                        -0.04347981584531405,
                        -0.04871464927421088,
                        -0.05392216701524391,
                        -0.059102001030734076,
                        -0.06425378614294777,
                        -0.06937716006492368,
                        -0.0744717634310085,
                        -0.07953723982710151,
                        -0.08457323582060713,
                        -0.08957940099008532,
                        -0.0945553879546049,
                        -0.09950085240279521,
                        -0.10441545312158886,
                        -0.10929885202465889,
                        -0.11415071418054586,
                        -0.11897070784046955,
                        -0.12375850446582674,
                        -0.12851377875536996,
                        -0.13323620867206598,
                        -0.1379254754696325,
                        -0.14258126371874613,
                        -0.14720326133292627,
                        -0.15179115959408562,
                        -0.1563446531777521,
                        -0.1608634401779522,
                        -0.16534722213175898,
                        -0.16979570404350305,
                        -0.1742085944086374,
                        -0.1785856052372652,
                        -0.18292645207731634,
                        -0.18723085403738016,
                        -0.1914985338091859,
                        -0.19572921768973583,
                        -0.19992263560307935,
                        -0.2040785211217362,
                        -0.20819661148776006,
                        -0.2122766476334446,
                        -0.21631837420166633,
                        -0.2203215395658675,
                        -0.2242858958496724,
                        -0.22821119894613873,
                        -0.2320972085366404,
                        -0.23594368810938146,
                        -0.23975040497753936,
                        -0.24351713029703415,
                        -0.24724363908392508,
                        -0.2509297102314311,
                        -0.2545751265265749,
                        -0.2581796746664452,
                        -0.2617431452740866,
                        -0.2652653329140002,
                        -0.268746036107266,
                        -0.2721850573462823,
                        -0.27558220310911713,
                        -0.2789372838734767,
                        -0.28225011413028456,
                        -0.2855205123968735,
                        -0.28874830122978795,
                        -0.29193330723719607,
                        -0.29507536109090926,
                        -0.2981742975380115,
                        -0.3012299554120938,
                        -0.3042421776440939
                      ],
                      "x": [
                        0,
                        0.010506998841437435,
                        0.02101399768287487,
                        0.031520996524312304,
                        0.04202799536574974,
                        0.05253499420718718,
                        0.06304199304862461,
                        0.07354899189006205,
                        0.08405599073149948,
                        0.09456298957293692,
                        0.10506998841437436,
                        0.1155769872558118,
                        0.12608398609724922,
                        0.13659098493868665,
                        0.1470979837801241,
                        0.15760498262156153,
                        0.16811198146299897,
                        0.1786189803044364,
                        0.18912597914587384,
                        0.19963297798731128,
                        0.21013997682874871,
                        0.22064697567018615,
                        0.2311539745116236,
                        0.24166097335306103,
                        0.25216797219449844,
                        0.2626749710359359,
                        0.2731819698773733,
                        0.2836889687188108,
                        0.2941959675602482,
                        0.30470296640168565,
                        0.31520996524312306,
                        0.3257169640845605,
                        0.33622396292599793,
                        0.34673096176743534,
                        0.3572379606088728,
                        0.3677449594503102,
                        0.3782519582917477,
                        0.3887589571331851,
                        0.39926595597462256,
                        0.40977295481605996,
                        0.42027995365749743,
                        0.43078695249893484,
                        0.4412939513403723,
                        0.4518009501818097,
                        0.4623079490232472,
                        0.4728149478646846,
                        0.48332194670612205,
                        0.49382894554755946,
                        0.5043359443889969,
                        0.5148429432304343,
                        0.5253499420718718,
                        0.5358569409133092,
                        0.5463639397547466,
                        0.5568709385961841,
                        0.5673779374376215,
                        0.5778849362790589,
                        0.5883919351204964,
                        0.5988989339619338,
                        0.6094059328033713,
                        0.6199129316448087,
                        0.6304199304862461,
                        0.6409269293276836,
                        0.651433928169121,
                        0.6619409270105584,
                        0.6724479258519959,
                        0.6829549246934333,
                        0.6934619235348707,
                        0.7039689223763081,
                        0.7144759212177456,
                        0.7249829200591831,
                        0.7354899189006204,
                        0.7459969177420579,
                        0.7565039165834954,
                        0.7670109154249328,
                        0.7775179142663702,
                        0.7880249131078076,
                        0.7985319119492451,
                        0.8090389107906826,
                        0.8195459096321199,
                        0.8300529084735574,
                        0.8405599073149949,
                        0.8510669061564322,
                        0.8615739049978697,
                        0.8720809038393071,
                        0.8825879026807446,
                        0.893094901522182,
                        0.9036019003636194,
                        0.9141088992050569,
                        0.9246158980464944,
                        0.9351228968879317,
                        0.9456298957293692,
                        0.9561368945708066,
                        0.9666438934122441,
                        0.9771508922536815,
                        0.9876578910951189,
                        0.9981648899365564,
                        1.0086718887779937,
                        1.0191788876194312,
                        1.0296858864608687,
                        1.0401928853023061,
                        1.0506998841437436,
                        1.061206882985181,
                        1.0717138818266183,
                        1.0822208806680558,
                        1.0927278795094932,
                        1.1032348783509307,
                        1.1137418771923682,
                        1.1242488760338056,
                        1.134755874875243,
                        1.1452628737166806,
                        1.1557698725581178,
                        1.1662768713995553,
                        1.1767838702409927,
                        1.1872908690824302,
                        1.1977978679238677,
                        1.2083048667653051,
                        1.2188118656067426,
                        1.2293188644481798,
                        1.2398258632896173,
                        1.2503328621310548,
                        1.2608398609724922,
                        1.2713468598139297,
                        1.2818538586553672,
                        1.2923608574968046,
                        1.302867856338242,
                        1.3133748551796793,
                        1.3238818540211168,
                        1.3343888528625543,
                        1.3448958517039917,
                        1.3554028505454292,
                        1.3659098493868667,
                        1.3764168482283041,
                        1.3869238470697414,
                        1.3974308459111788,
                        1.4079378447526163,
                        1.4184448435940538,
                        1.4289518424354912,
                        1.4394588412769287,
                        1.4499658401183662,
                        1.4604728389598036,
                        1.4709798378012409,
                        1.4814868366426783,
                        1.4919938354841158,
                        1.5025008343255533,
                        1.5130078331669907,
                        1.5235148320084282,
                        1.5340218308498657,
                        1.544528829691303,
                        1.5550358285327404,
                        1.5655428273741778,
                        1.5760498262156153,
                        1.5865568250570528,
                        1.5970638238984902,
                        1.6075708227399277,
                        1.6180778215813651,
                        1.6285848204228024,
                        1.6390918192642399,
                        1.6495988181056773,
                        1.6601058169471148,
                        1.6706128157885523,
                        1.6811198146299897,
                        1.6916268134714272,
                        1.7021338123128644,
                        1.712640811154302,
                        1.7231478099957394,
                        1.7336548088371768,
                        1.7441618076786143,
                        1.7546688065200517,
                        1.7651758053614892,
                        1.7756828042029267,
                        1.786189803044364,
                        1.7966968018858014,
                        1.8072038007272389,
                        1.8177107995686763,
                        1.8282177984101138,
                        1.8387247972515512,
                        1.8492317960929887,
                        1.859738794934426,
                        1.8702457937758634,
                        1.8807527926173009,
                        1.8912597914587383,
                        1.9017667903001758,
                        1.9122737891416133,
                        1.9227807879830507,
                        1.9332877868244882,
                        1.9437947856659255,
                        1.954301784507363,
                        1.9648087833488004,
                        1.9753157821902378,
                        1.9858227810316753,
                        1.9963297798731128,
                        2.00683677871455,
                        2.0173437775559875,
                        2.027850776397425,
                        2.0383577752388624,
                        2.0488647740803,
                        2.0593717729217373,
                        2.069878771763175,
                        2.0803857706046123,
                        2.0908927694460497,
                        2.101399768287487,
                        2.1119067671289247,
                        2.122413765970362,
                        2.1329207648117996,
                        2.1434277636532366,
                        2.153934762494674,
                        2.1644417613361115,
                        2.174948760177549,
                        2.1854557590189865,
                        2.195962757860424,
                        2.2064697567018614,
                        2.216976755543299,
                        2.2274837543847363,
                        2.237990753226174,
                        2.2484977520676113,
                        2.2590047509090487,
                        2.269511749750486,
                        2.2800187485919237,
                        2.290525747433361,
                        2.301032746274798,
                        2.3115397451162356,
                        2.322046743957673,
                        2.3325537427991105,
                        2.343060741640548,
                        2.3535677404819855,
                        2.364074739323423,
                        2.3745817381648604,
                        2.385088737006298,
                        2.3955957358477353,
                        2.406102734689173,
                        2.4166097335306103,
                        2.4271167323720477,
                        2.437623731213485,
                        2.4481307300549227,
                        2.4586377288963597,
                        2.469144727737797,
                        2.4796517265792346,
                        2.490158725420672,
                        2.5006657242621095,
                        2.511172723103547,
                        2.5216797219449845,
                        2.532186720786422,
                        2.5426937196278594,
                        2.553200718469297,
                        2.5637077173107343,
                        2.574214716152172,
                        2.5847217149936093,
                        2.5952287138350467,
                        2.605735712676484,
                        2.616242711517921,
                        2.6267497103593587,
                        2.637256709200796,
                        2.6477637080422336,
                        2.658270706883671,
                        2.6687777057251085,
                        2.679284704566546,
                        2.6897917034079835,
                        2.700298702249421,
                        2.7108057010908584,
                        2.721312699932296,
                        2.7318196987737333,
                        2.742326697615171,
                        2.7528336964566082,
                        2.7633406952980457,
                        2.7738476941394827,
                        2.78435469298092,
                        2.7948616918223577,
                        2.805368690663795,
                        2.8158756895052326,
                        2.82638268834667,
                        2.8368896871881075,
                        2.847396686029545,
                        2.8579036848709825,
                        2.86841068371242,
                        2.8789176825538574,
                        2.889424681395295,
                        2.8999316802367323,
                        2.9104386790781698,
                        2.9209456779196072,
                        2.9314526767610443,
                        2.9419596756024817,
                        2.952466674443919,
                        2.9629736732853567,
                        2.973480672126794,
                        2.9839876709682316,
                        2.994494669809669,
                        3.0050016686511065,
                        3.015508667492544,
                        3.0260156663339814,
                        3.036522665175419,
                        3.0470296640168564,
                        3.057536662858294,
                        3.0680436616997313,
                        3.0785506605411688,
                        3.089057659382606,
                        3.0995646582240433,
                        3.1100716570654807,
                        3.120578655906918,
                        3.1310856547483557,
                        3.141592653589793
                      ],
                      "line": {
                        "shape": "spline"
                      },
                      "type": "scatter"
                    }
                  ],
                  "config": {
                    "plotlyServerURL": "https://plot.ly",
                    "linkText": "Export to plot.ly",
                    "showLink": false
                  },
                  "layout": {
                    "yaxis": {
                      "title": {
                        "text": "<i>(nanoseconds),/i>"
                      }
                    },
                    "xaxis": {
                      "title": {
                        "text": "<i> (nanoseconds)</i>"
                      }
                    },
                    "template": {
                      "layout": {
                        "shapedefaults": {
                          "line": {
                            "color": "#2a3f5f"
                          }
                        },
                        "polar": {
                          "radialaxis": {
                            "ticks": "",
                            "gridcolor": "white",
                            "linecolor": "white"
                          },
                          "bgcolor": "#E5ECF6",
                          "angularaxis": {
                            "ticks": "",
                            "gridcolor": "white",
                            "linecolor": "white"
                          }
                        },
                        "colorway": [
                          "#636efa",
                          "#EF553B",
                          "#00cc96",
                          "#ab63fa",
                          "#FFA15A",
                          "#19d3f3",
                          "#FF6692",
                          "#B6E880",
                          "#FF97FF",
                          "#FECB52"
                        ],
                        "xaxis": {
                          "automargin": true,
                          "title": {
                            "standoff": 15
                          },
                          "zerolinewidth": 2,
                          "ticks": "",
                          "zerolinecolor": "white",
                          "gridcolor": "white",
                          "linecolor": "white"
                        },
                        "colorscale": {
                          "diverging": [
                            [
                              0,
                              "#8e0152"
                            ],
                            [
                              0.1,
                              "#c51b7d"
                            ],
                            [
                              0.2,
                              "#de77ae"
                            ],
                            [
                              0.3,
                              "#f1b6da"
                            ],
                            [
                              0.4,
                              "#fde0ef"
                            ],
                            [
                              0.5,
                              "#f7f7f7"
                            ],
                            [
                              0.6,
                              "#e6f5d0"
                            ],
                            [
                              0.7,
                              "#b8e186"
                            ],
                            [
                              0.8,
                              "#7fbc41"
                            ],
                            [
                              0.9,
                              "#4d9221"
                            ],
                            [
                              1,
                              "#276419"
                            ]
                          ],
                          "sequential": [
                            [
                              0,
                              "#0d0887"
                            ],
                            [
                              0.1111111111111111,
                              "#46039f"
                            ],
                            [
                              0.2222222222222222,
                              "#7201a8"
                            ],
                            [
                              0.3333333333333333,
                              "#9c179e"
                            ],
                            [
                              0.4444444444444444,
                              "#bd3786"
                            ],
                            [
                              0.5555555555555556,
                              "#d8576b"
                            ],
                            [
                              0.6666666666666666,
                              "#ed7953"
                            ],
                            [
                              0.7777777777777778,
                              "#fb9f3a"
                            ],
                            [
                              0.8888888888888888,
                              "#fdca26"
                            ],
                            [
                              1,
                              "#f0f921"
                            ]
                          ],
                          "sequentialminus": [
                            [
                              0,
                              "#0d0887"
                            ],
                            [
                              0.1111111111111111,
                              "#46039f"
                            ],
                            [
                              0.2222222222222222,
                              "#7201a8"
                            ],
                            [
                              0.3333333333333333,
                              "#9c179e"
                            ],
                            [
                              0.4444444444444444,
                              "#bd3786"
                            ],
                            [
                              0.5555555555555556,
                              "#d8576b"
                            ],
                            [
                              0.6666666666666666,
                              "#ed7953"
                            ],
                            [
                              0.7777777777777778,
                              "#fb9f3a"
                            ],
                            [
                              0.8888888888888888,
                              "#fdca26"
                            ],
                            [
                              1,
                              "#f0f921"
                            ]
                          ]
                        },
                        "paper_bgcolor": "white",
                        "plot_bgcolor": "#E5ECF6",
                        "title": {
                          "x": 0.05
                        },
                        "scene": {
                          "zaxis": {
                            "backgroundcolor": "#E5ECF6",
                            "ticks": "",
                            "gridwidth": 2,
                            "showbackground": true,
                            "zerolinecolor": "white",
                            "gridcolor": "white",
                            "linecolor": "white"
                          },
                          "xaxis": {
                            "backgroundcolor": "#E5ECF6",
                            "ticks": "",
                            "gridwidth": 2,
                            "showbackground": true,
                            "zerolinecolor": "white",
                            "gridcolor": "white",
                            "linecolor": "white"
                          },
                          "yaxis": {
                            "backgroundcolor": "#E5ECF6",
                            "ticks": "",
                            "gridwidth": 2,
                            "showbackground": true,
                            "zerolinecolor": "white",
                            "gridcolor": "white",
                            "linecolor": "white"
                          }
                        },
                        "yaxis": {
                          "automargin": true,
                          "title": {
                            "standoff": 15
                          },
                          "zerolinewidth": 2,
                          "ticks": "",
                          "zerolinecolor": "white",
                          "gridcolor": "white",
                          "linecolor": "white"
                        },
                        "annotationdefaults": {
                          "arrowwidth": 1,
                          "arrowhead": 0,
                          "arrowcolor": "#2a3f5f"
                        },
                        "hoverlabel": {
                          "align": "left"
                        },
                        "ternary": {
                          "bgcolor": "#E5ECF6",
                          "baxis": {
                            "ticks": "",
                            "gridcolor": "white",
                            "linecolor": "white"
                          },
                          "caxis": {
                            "ticks": "",
                            "gridcolor": "white",
                            "linecolor": "white"
                          },
                          "aaxis": {
                            "ticks": "",
                            "gridcolor": "white",
                            "linecolor": "white"
                          }
                        },
                        "mapbox": {
                          "style": "light"
                        },
                        "hovermode": "closest",
                        "font": {
                          "color": "#2a3f5f"
                        },
                        "geo": {
                          "showland": true,
                          "landcolor": "#E5ECF6",
                          "showlakes": true,
                          "bgcolor": "white",
                          "subunitcolor": "white",
                          "lakecolor": "white"
                        },
                        "coloraxis": {
                          "colorbar": {
                            "outlinewidth": 0,
                            "ticks": ""
                          }
                        }
                      },
                      "data": {
                        "mesh3d": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "mesh3d"
                          }
                        ],
                        "scattercarpet": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scattercarpet"
                          }
                        ],
                        "pie": [
                          {
                            "automargin": true,
                            "type": "pie"
                          }
                        ],
                        "surface": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "surface",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "table": [
                          {
                            "header": {
                              "line": {
                                "color": "white"
                              },
                              "fill": {
                                "color": "#C8D4E3"
                              }
                            },
                            "cells": {
                              "line": {
                                "color": "white"
                              },
                              "fill": {
                                "color": "#EBF0F8"
                              }
                            },
                            "type": "table"
                          }
                        ],
                        "scatterpolargl": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scatterpolargl"
                          }
                        ],
                        "contour": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "contour",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "carpet": [
                          {
                            "type": "carpet",
                            "baxis": {
                              "minorgridcolor": "white",
                              "gridcolor": "white",
                              "linecolor": "white",
                              "endlinecolor": "#2a3f5f",
                              "startlinecolor": "#2a3f5f"
                            },
                            "aaxis": {
                              "minorgridcolor": "white",
                              "gridcolor": "white",
                              "linecolor": "white",
                              "endlinecolor": "#2a3f5f",
                              "startlinecolor": "#2a3f5f"
                            }
                          }
                        ],
                        "contourcarpet": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "contourcarpet"
                          }
                        ],
                        "heatmap": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "heatmap",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "scattermapbox": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scattermapbox"
                          }
                        ],
                        "scatter3d": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "line": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scatter3d"
                          }
                        ],
                        "scattergl": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scattergl"
                          }
                        ],
                        "scatterternary": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scatterternary"
                          }
                        ],
                        "histogram": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "histogram"
                          }
                        ],
                        "heatmapgl": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "heatmapgl",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "scatterpolar": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scatterpolar"
                          }
                        ],
                        "histogram2d": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "histogram2d",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "scattergeo": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scattergeo"
                          }
                        ],
                        "bar": [
                          {
                            "marker": {
                              "line": {
                                "color": "#E5ECF6",
                                "width": 0.5
                              }
                            },
                            "type": "bar",
                            "error_x": {
                              "color": "#2a3f5f"
                            },
                            "error_y": {
                              "color": "#2a3f5f"
                            }
                          }
                        ],
                        "choropleth": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "choropleth"
                          }
                        ],
                        "parcoords": [
                          {
                            "line": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "parcoords"
                          }
                        ],
                        "barpolar": [
                          {
                            "marker": {
                              "line": {
                                "color": "#E5ECF6",
                                "width": 0.5
                              }
                            },
                            "type": "barpolar"
                          }
                        ],
                        "histogram2dcontour": [
                          {
                            "colorbar": {
                              "outlinewidth": 0,
                              "ticks": ""
                            },
                            "type": "histogram2dcontour",
                            "colorscale": [
                              [
                                0,
                                "#0d0887"
                              ],
                              [
                                0.1111111111111111,
                                "#46039f"
                              ],
                              [
                                0.2222222222222222,
                                "#7201a8"
                              ],
                              [
                                0.3333333333333333,
                                "#9c179e"
                              ],
                              [
                                0.4444444444444444,
                                "#bd3786"
                              ],
                              [
                                0.5555555555555556,
                                "#d8576b"
                              ],
                              [
                                0.6666666666666666,
                                "#ed7953"
                              ],
                              [
                                0.7777777777777778,
                                "#fb9f3a"
                              ],
                              [
                                0.8888888888888888,
                                "#fdca26"
                              ],
                              [
                                1,
                                "#f0f921"
                              ]
                            ]
                          }
                        ],
                        "scatter": [
                          {
                            "marker": {
                              "colorbar": {
                                "outlinewidth": 0,
                                "ticks": ""
                              }
                            },
                            "type": "scatter"
                          }
                        ]
                      }
                    },
                    "title": {
                      "text": "<b>ILLUSTRATION</b>"
                    }
                  }
                }
              }
            ],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_4823e3f6ee9040b28f7140a2a050a083",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "89abfec08149443cb3507dc20de35d15": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "state": {
            "_view_name": "StyleView",
            "_model_name": "DescriptionStyleModel",
            "description_width": "",
            "_view_module": "@jupyter-widgets/base",
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.2.0",
            "_model_module": "@jupyter-widgets/controls"
          }
        },
        "98fa4f19090342a8b42152ad2bfa5390": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4e9ba8db56a948fa96f5681739287dc1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "state": {
            "_view_name": "StyleView",
            "handle_color": null,
            "_model_name": "SliderStyleModel",
            "description_width": "",
            "_view_module": "@jupyter-widgets/base",
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.2.0",
            "_model_module": "@jupyter-widgets/controls"
          }
        },
        "7dc19eb7edd54b68bcda4235ac8ada9d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4823e3f6ee9040b28f7140a2a050a083": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/SansBasnet/Python-automation/blob/master/Bessel_function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oOCV9pUoUDde",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "outputId": "940b2df9-6477-474f-a762-285a08b8147d"
      },
      "source": [
        "import plotly as py\n",
        "import plotly.graph_objs as go\n",
        "import ipywidgets as widgets\n",
        "import numpy as np\n",
        "\n",
        "from scipy import special \n",
        "\n",
        "py.offline.init_notebook_mode(connected=True)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "        <script type=\"text/javascript\">\n",
              "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
              "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
              "        if (typeof require !== 'undefined') {\n",
              "        require.undef(\"plotly\");\n",
              "        requirejs.config({\n",
              "            paths: {\n",
              "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
              "            }\n",
              "        });\n",
              "        require(['plotly'], function(Plotly) {\n",
              "            window._Plotly = Plotly;\n",
              "        });\n",
              "        }\n",
              "        </script>\n",
              "        "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SwyRWMLyUWWo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 668,
          "referenced_widgets": [
            "d1e107d52a21498fadea284fa6923d66",
            "ef0644985e5f420186b72827c8b45487",
            "1c34112811cf40c6b25d350d6339a781",
            "a7497ed2202c4f71a3038ca14dce5a9f",
            "42d210a862ad4618946c2b6adc56c35f",
            "89abfec08149443cb3507dc20de35d15",
            "98fa4f19090342a8b42152ad2bfa5390",
            "4e9ba8db56a948fa96f5681739287dc1",
            "7dc19eb7edd54b68bcda4235ac8ada9d",
            "4823e3f6ee9040b28f7140a2a050a083"
          ]
        },
        "outputId": "c9710574-d51a-4931-ebce-ae970ad76784"
      },
      "source": [
        "x = np.linspace(0, np.pi, 300)\n",
        "\n",
        "layout = go.Layout(\n",
        "    \n",
        "    title='<b>ILLUSTRATION</b>',\n",
        "    yaxis = dict(\n",
        "        title='<i>(nanoseconds),/i>'\n",
        "    ),\n",
        "    xaxis=  dict(\n",
        "        title = '<i> (nanoseconds)</i>'\n",
        "    )\n",
        ")\n",
        "\n",
        "def update_plot(signals, freq):\n",
        "  data = []\n",
        "  for s in signals:\n",
        "    trace1 = go.Scatter(\n",
        "        x=x,\n",
        "        y=special.jv(s, freq * x),\n",
        "        mode='lines',\n",
        "        name='Bessel{}'. format(s),\n",
        "        line =dict(\n",
        "            shape = 'spline'\n",
        "        )\n",
        "    )\n",
        "    data.append(trace1)\n",
        "\n",
        "  fig =go.Figure(data = data, layout = layout)\n",
        "  py.offline.iplot(fig)\n",
        "\n",
        "signals = widgets.SelectMultiple(options=list(range(6)), value=(0, ), description='Bessel Order')\n",
        "freq = widgets.FloatSlider(min=1, max =20, value =1, description ='Freq')\n",
        "widgets.interactive(update_plot, signals=signals, freq=freq)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "d1e107d52a21498fadea284fa6923d66",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(SelectMultiple(description='Bessel Order', index=(0,), options=(0, 1, 2, 3, 4, 5), value…"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EUiTEOfZWCWZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}