Data update

Task/Gamma-function/DuckDB/gamma-function.duckdb

@@ -0,0 +1,30 @@
+create or replace function gamma_taylor(x) as (
+  select gamma
+  from ( select [
+    1.00000000000000000000,  0.57721566490153286061,  -0.65587807152025388108, -0.04200263503409523553,
+    0.16653861138229148950, -0.04219773455554433675,  -0.00962197152787697356,  0.00721894324666309954,
+   -0.00116516759185906511, -0.00021524167411495097,   0.00012805028238811619, -0.00002013485478078824,
+   -0.00000125049348214267,  0.00000113302723198170,  -0.00000020563384169776,  0.00000000611609510448,
+    0.00000000500200764447, -0.00000000118127457049,   0.00000000010434267117,  0.00000000000778226344,
+   -0.00000000000369680562,  0.00000000000051003703,  -0.00000000000002058326, -0.00000000000000534812,
+    0.00000000000000122678, -0.00000000000000011813,   0.00000000000000000119,  0.00000000000000000141,
+   -0.00000000000000000023,  0.00000000000000000002
+    ] as a,
+    length(a) as n,
+    (with recursive cte as (
+       select 2 as an, a[n] as acc
+       union all
+       select an+1 as an,
+         (acc * (x-1)) + a[1 + n-an] as acc
+       from cte
+       where an <= n
+     )
+     select 1 / last(acc order by an) from cte) as gamma
+  )
+  limit 1
+);
+
+## Comparison
+select x, gamma, taylor, 2 * @(gamma-taylor)/(gamma+taylor) as "%"
+from (select x, gamma(x) as gamma, gamma_taylor(x) as taylor
+      from (select x/3 as x from range(1,11) t(x))) ;

Task/Gamma-function/FutureBasic/gamma-function.basic

@@ -0,0 +1,35 @@
+include "NSLog.incl"
+
+#define FB_M_E 2.7182818284590452
+
+double local fn StirlingGamma( x as double )
+  return fn sqrt(2 * M_PI / x ) * fn pow(x / FB_M_E, x )
+end fn = 0.0
+
+double local fn LanczosGamma( x as double )
+  int g = 7
+  static double p(8) = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,¬
+  771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012,¬
+  9.9843695780195716e-6, 1.5056327351493116e-7}
+
+  if ( x < 0.5 ) then return M_PI / ( sin( M_PI * x ) * fn LanczosGamma( 1 - x ) )
+  x -= 1.0
+  double a = p(0)
+  for int i = 1 to 8
+    a += p(i) / ( x + i )
+  next
+  double t = x + g + 0.5
+  return fn sqrt(2 * M_PI ) * fn pow(t, x + 0.5 ) * exp(-t ) * a
+end fn = 0.0
+
+void local fn RunGammaFunctions
+  NSLog( @"Gamma\tStirling\t\t\t Lanczos" )
+  for double i = 1.0 to 20
+    double value = i / 10.0
+    NSLog( @"%1.2f\t%17.15f\t %1.15f", value, fn StirlingGamma( value ), fn LanczosGamma( value ) )
+  next
+end fn
+
+fn RunGammaFunctions
+
+HandleEvents

Task/Gamma-function/Pluto/gamma-function.pluto

@@ -0,0 +1,12 @@
+local fmt = require "fmt"
+require "math2"
+
+local function stirling(x)
+    return math.sqrt(2 * math.pi / x) * ((x / math.e) ^ x)
+end
+
+print(" x\tStirling\t\tLanczos\n")
+for i = 1, 20 do
+    local d = i / 10
+    fmt.print("%4.2f\t%0.14f\t%0.14f", d, stirling(d), math.gamma(d))
+end

Task/Gamma-function/REXX/gamma-function.rexx

@@ -1,10 +1,13 @@
--- 8 May 2025
+-- 28 Jul 2025
 include Settings
+arg n
+if n = '' then
+   n = 100
+numeric digits n
 
 say 'GAMMA'
 say version
 say
-arg n; if n = '' then n = 100; numeric digits n
 say '(Half)integers formulas'
 w = '-99.5 -10.5 -5.5 -2.5 -1.5 -0.5 0.5 1 1.5 2 2.5 5 5.5 10 10.5 99 99.5'
 numeric digits n
@@ -47,12 +50,8 @@ end
 exit
 
 Stirling:
-procedure expose glob. fact.
+procedure expose Memo. fact.
 arg x
 return Sqrt(2*Pi()/x) * Power(x/e(),x)
 
-include Constants
-include Functions
-include Special
-include Numbers
-include Abend
+include Math