..
  Copyright 1988-2021 Free Software Foundation, Inc.
  This is part of the GCC manual.
  For copying conditions, see the GPL license file

.. _gamma:

GAMMA --- Gamma function
************************

.. index:: GAMMA

.. index:: DGAMMA

.. index:: Gamma function

.. index:: Factorial function

.. function:: GAMMA(X)

  ``GAMMA(X)`` computes Gamma (\Gamma) of :samp:`{X}`. For positive,
  integer values of :samp:`{X}` the Gamma function simplifies to the factorial
  function \Gamma(x)=(x-1)!.

  :param X:
    Shall be of type ``REAL`` and neither zero
    nor a negative integer.

  :return:
    The return value is of type ``REAL`` of the same kind as :samp:`{X}`.

  :samp:`{Standard}:`
    Fortran 2008 and later

  :samp:`{Class}:`
    Elemental function

  :samp:`{Syntax}:`

  .. code-block:: fortran

    X = GAMMA(X)

  :samp:`{Example}:`

    .. code-block:: fortran

      program test_gamma
        real :: x = 1.0
        x = gamma(x) ! returns 1.0
      end program test_gamma

  :samp:`{Specific names}:`
    =============  =============  ===========  =============
    Name           Argument       Return type  Standard
    =============  =============  ===========  =============
    ``DGAMMA(X)``  ``REAL(8) X``  ``REAL(8)``  GNU extension
    =============  =============  ===========  =============

  :samp:`{See also}:`
    Logarithm of the Gamma function: 
    LOG_GAMMA