tgamma

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

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():
           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L

DESCRIPTION
       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)

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 oc-
       curs, 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  re-
       turn 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 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
       POSIX.1-2001.

       Range error: result underflow
              An underflow floating-point exception (FE_UNDERFLOW) is  raised,
              and errno is set to ERANGE.

VERSIONS
       These functions first appeared in glibc in version 2.1.

ATTRIBUTES
       For  an  explanation  of  the  terms  used  in  this  section,  see at-
       tributes(7).

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

NOTES
       This function had to be called "true gamma function" since there is al-
       ready a function gamma(3) that returns something else (see gamma(3) for
       details).

BUGS
       Before version 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.  x

       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 ex-
       ception raised), rather than a pole error.

SEE ALSO
       gamma(3), lgamma(3)

COLOPHON
       This page is part of release 5.05 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
       https://www.kernel.org/doc/man-pages/.

GNU                               2017-09-15                         TGAMMA(3)