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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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