# tgamma(3) — Linux manual page

```TGAMMA(3)                 Linux Programmer's Manual                TGAMMA(3)
```

## NAME         top

```       tgamma, tgammaf, tgammal - true gamma function
```

## SYNOPSIS         top

```       #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         top

```       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         top

```       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         top

```       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         top

```       These functions first appeared in glibc in version 2.1.
```

## ATTRIBUTES         top

```       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         top

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