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.

# 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 glibc 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.

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.