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);

       Link with -lm.

   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:

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

CONFORMING TO

       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.

SEE ALSO

       gamma(3), lgamma(3)

COLOPHON

       This  page  is  part of release 4.15 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/.