tgamma(3) Library Functions Manual tgamma(3)

# NAME

tgamma, tgammaf, tgammal - true gamma function

# LIBRARY

Math library (libm, -lm)

# 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:

errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
errno is set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
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.

An underflow floating-point exception (FE_UNDERFLOW) is raised, and errno is set to ERANGE.

# VERSIONS

These functions were added in glibc 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

# STANDARDS

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

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).

 2022-12-15 Linux man-pages 6.02