tgamma, tgammaf, tgammal - true gamma function

       For an explanation of the terms used in this section, see attributes(7).
       ┌─────────────────────────────────────────────────────────────────────────────┬───────────────┬─────────┐
       │ Interface                                                                   │ Attribute     │ Value   │
       ├─────────────────────────────────────────────────────────────────────────────┼───────────────┼─────────┤
       │ tgamma(), tgammaf(), tgammal()                                              │ Thread safety │ MT-Safe │
       └─────────────────────────────────────────────────────────────────────────────┴───────────────┴─────────┘

       Before  glibc  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.

       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.

       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)

       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.

       glibc 2.1.  C99, POSIX.1-2001.

       Math library (libm, -lm)

       tgamma, tgammaf, tgammal - true gamma function

       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).

       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.

gamma(3), lgamma(3)

Linux man-pages 6.9.1                              2024-05-02                                          tgamma(3)

       C11, POSIX.1-2008.

#include<math.h>doubletgamma(doublex);floattgammaf(floatx);longdoubletgammal(longdoublex);

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

       tgamma(), tgammaf(), tgammal():
           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L