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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);

       Link with -lm.

   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

       tgamma(), tgammaf(), tgammal():
           _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE ||
           _POSIX_C_SOURCE >= 200112L;
           or cc -std=c99

DESCRIPTION

       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.

              errno is not set for this case.

VERSIONS

       These functions first appeared in glibc in version 2.1.

CONFORMING TO

       C99, POSIX.1-2001.

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

       If x is negative infinity, errno is not set (it should be set to EDOM).

       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

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       description of the project, and information about reporting  bugs,  can
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