TGAMMA

NAME

tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS

#include <math.h>

double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);

DESCRIPTION

The Gamma function is defined by

Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt

It is defined for every real number except for nonpositive integers. For nonnegative integral m one has

Gamma(m+1) = m!

and, more generally, for all x:

Gamma(x+1) = x * Gamma(x)

For x < 0.5 one can use

Gamma(x) * Gamma(1-x) = PI/sin(PI*x)

This function returns the value of the Gamma function for the argument x. It had to be called "true gamma function" since there is already a function gamma() that returns something else.

ERRORS

An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

A range error occurs if x is too large. A pole error occurs if x is zero. A domain error (or a pole error) occurs if x is a negative integer.

CONFORMING TO

C99.