Gamma Simple

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A Sterling series approximation of the gamma function.

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Gamma Simple
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Gamma Simple

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doublegamma_simple( double x )[inline]

Returns a simple approximation to the gamma functions. If your only interested in low levels of accuracy (10 significant figures), then this solution is evaluated quickly and is relatively stable.

This approximation of the gamma function is achieved using the exponential of the Stirling series,

$\Gamma(z) = e^{\ln |\Gamma(z)|}$

(1)

where

$ln \Gamma(z) = \frac{1}{2} \ln(2 \pi) + (z - \frac{1}{2}) \ln z - z + \frac{1}{12z} - \frac{1}{360 z^3} + \frac{1}{1260 z^5} - ...$

(2)

Example 1

#include <codecogs/maths/special/gamma/gamma_simple.h>
#include <stdio.h>
 
int main()
{
  for(double x=3; x<7; x+=0.4)
  printf("\n x=%lf gamma_simple=%lf",x, Maths::Special::Gamma::gamma_simple(x));
  return 0;
}

Output:

x=3.000000 gamma_simple=2.000000
x=3.400000 gamma_simple=2.981206
x=3.800000 gamma_simple=4.694174
x=4.200000 gamma_simple=7.756690
x=4.600000 gamma_simple=13.381286
x=5.000000 gamma_simple=24.000000
x=5.400000 gamma_simple=44.598848
x=5.800000 gamma_simple=85.621738
x=6.200000 gamma_simple=169.406099
x=6.600000 gamma_simple=344.701924

Parameters

argument

Authors

Tony Ottosson and Pal Frenger
Documention by Will Bateman (August 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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