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#### 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 5.02 of the Linux man-pages project.  A description of the