TGAMMA(3)                  Linux Programmer's Manual                 TGAMMA(3)

       tgamma, tgammaf, tgammal - true gamma function

       #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

       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

           Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

       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 math-
       ematical 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.

       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  excep-
              tion (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

       Range error: result underflow
              An underflow floating-point exception (FE_UNDERFLOW) is raised.

              errno is not set for this case.

       These functions first appeared in glibc in version 2.1.

       For   an   explanation   of   the  terms  used  in  this  section,  see

       |Interface                      | Attribute     | Value   |
       |tgamma(), tgammaf(), tgammal() | Thread safety | MT-Safe |
       C99, POSIX.1-2001, POSIX.1-2008.

       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).

       Before version 2.18, the glibc implementation of  these  functions  did
       not set errno to EDOM when x is negative infinity.

       In  glibc  versions  2.3.3  and earlier, an argument of +0 or -0 incor-
       rectly produced a domain error (errno set to  EDOM  and  an  FE_INVALID
       exception raised), rather than a pole error.

       gamma(3), lgamma(3)

       This  page  is  part of release 4.04 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

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