Added asymptotics for Stirling factorials, partitions and primes comp…

…osition
fargolo · Sep 23, 2023 · c7b4d16 · c7b4d16
1 parent 56ee9a9
commit c7b4d16
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Showing 4 changed files with 30 additions and 11 deletions.
diff --git a/README.md b/README.md
@@ -41,8 +41,9 @@ julia>p_binary_words_runl(6,200)
 0.166...
 ```
 
-
-
-
-
+Stirling approximation for n!:
+```
+julia> stirling_factorial(7)
+4980.395831612462
+```
 
diff --git a/src/AnalyticComb.jl b/src/AnalyticComb.jl
@@ -4,10 +4,11 @@ using SymPy
 #using TaylorSeries
 #using DynamicalSystems
 
-export 
+export
+	stirling_factorial, partitions, primes_composition
 	p_binary_words_runl
 
 include("binary_words.jl")
-#include("inference_plot.jl")
+include("asymptotics.jl")
 
 end
diff --git a/src/asymptotics.jl b/src/asymptotics.jl
@@ -0,0 +1,22 @@
+"""
+    stirling_factorial(n)
+
+Stirling approximation for n! as (n/exp(1))^n*sqrt(2*pi*n).
+"""
+stirling_factorial(n) = (n/exp(1))^n*sqrt(2*pi*n)
+
+
+"""
+    partitions(n)
+
+Asymptotics for partition of integers by Hardy and Ramanujan, later improved by Rademache
+"""
+partitions(n) = (1/(4*n*sqrt(3)))*exp(pi*sqrt(2n/3))
+
+
+"""
+    primes_composition(n)
+
+Asymptotics for composition of primes.
+"""
+primes_composition(n) = 0.30365 * 1.47622^n
diff --git a/src/binary_words.jl b/src/binary_words.jl
@@ -1,8 +1,3 @@
-
-
-
-
-
 """
     W_coeff(r;n_tot=200)