Evaluates the incomplete gamma function γ(a, x).
Synopsis
#include <imsls.h>
float imsls_f_gamma_incomplete (float a, float x)
The type double procedure is imsls_d_gamma_incomplete.
Required Arguments
float a
(Input)
Parameter of the incomplete gamma function is to be evaluated. It
must be positive.
float x
(Input)
Point at which the incomplete gamma function is to be evaluated. It
must be nonnegative.
Return Value
The value of the incomplete gamma function γ(a, x).
Description
The incomplete gamma function, γ(a, x), is defined to be
for x > 0. The incomplete gamma
function is defined only for a > 0. Although
γ(a, x)
is well defined for x > −∞, this algorithm
does not calculate γ(a, x)
for negative x. For large a and sufficiently large x,
γ(a, x)
may overflow. γ(a, x)
is bounded by Γ(a), and
users may find this bound a useful guide in determining legal values for
a.
Figure 15- 3 Contour Plot of γ(a, x)
Example
Evaluates the incomplete gamma function at a = 1 and x = 3.
#include <stdio.h>
#include <imsls.h>
int main()
{
float x = 3.0;
float a = 1.0;
float ans;
ans = imsls_f_gamma_incomplete(a, x);
printf("incomplete gamma(%f,%f) = %f\n", a, x, ans);
}
Output
incomplete gamma(1.000000,3.000000) = 0.950213
Fatal Errors
IMSLS_NO_CONV_200_TS_TERMS The function did not converge in 200 terms of Taylor series.
IMSLS_NO_CONV_200_CF_TERMS The function did not converge in 200 terms of the continued fraction.
