# tgammal(3)

#### 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)

```

#### RETURNVALUE

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

#### CONFORMINGTO

```   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.

```

#### SEEALSO

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

```

#### COLOPHON

```   This page is part of release 4.09 of the Linux  man-pages  project.   A
description  of  the project, information about reporting bugs, and the
latest    version    of    this    page,    can     be     found     at
https://www.kernel.org/doc/man-pages/.
```

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