# 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);

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

# DESCRIPTION

These functions calculate the Gamma function of x.
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)
Furthermore, the following is valid for all values of x outside the poles:
Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

# RETURN VALUE

On success, these functions return Gamma(x).
If x is a NaN, a NaN is returned.
If x is positive infinity, positive infinity is returned.
If x is a negative integer, or is negative infinity, a domain error occurs, and a NaN is returned.
If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.
If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
If x is -0 or +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.

# ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.
The following errors can occur:
Domain error: x is a negative integer, or negative infinity
errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
Pole error: x is +0 or -0
errno is set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
Range error: result overflow
errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.
glibc also gives the following error which is not specified in C99 or POSIX.1-2001.
Range error: result underflow
An underflow floating-point exception (FE_UNDERFLOW) is raised, and errno is set to ERANGE.

# VERSIONS

These functions first appeared in glibc in version 2.1.

# ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).
 Interface Attribute Value tgamma (), tgammaf (), tgammal () Thread safety MT-Safe

# CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

# NOTES

This function had to be called "true gamma function" since there is already a function gamma(3) that returns something else (see gamma(3) for details).

# BUGS

Before version 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity.
Before glibc 2.19, the glibc implementation of these functions did not set errno to ERANGE on an underflow range error. x
In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error.

gamma(3), lgamma(3)

### Information

Source
Linux kernel
OS/version
GNU
Source updated
September 15, 2017
Page created
February 9, 2018
Page generated
December 2, 2018