# tgamma(3) — Linux manual page

```tgamma(3)               Library Functions Manual               tgamma(3)
```

## NAME         top

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

## LIBRARY         top

```       Math library (libm, -lm)
```

## 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.
```

## 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 │
└─────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       C11, POSIX.1-2008.
```

## HISTORY         top

```       glibc 2.1.  C99, POSIX.1-2001.
```

## NOTES         top

```       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         top

```       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.
```

```       gamma(3), lgamma(3)
```

## COLOPHON         top

```       This page is part of the man-pages (Linux kernel and C library
user-space interface documentation) project.  Information about
the project can be found at
⟨https://www.kernel.org/doc/man-pages/⟩.  If you have a bug report
for this manual page, see
⟨https://git.kernel.org/pub/scm/docs/man-pages/man-pages.git/tree/CONTRIBUTING⟩.