NAME
tgamma, tgammaf, tgammal - true gamma function
SYNOPSIS
#include <math.h>
I double tgamma(double x );
I float tgammaf(float x );
I long double tgammal(long double x );
Compile with -std=c99; link with -lm.
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 non-positive integers.
For non-negative integral m one has
Gamma(m+1) = m!
and, more generally, for all x:
Gamma(x+1) = x * Gamma(x)
Furthermore, the following is valid for all values of x
outside the poles:
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(3)
that returns something else.
ERRORS
In order to check for errors, 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.
SEE ALSO
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