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

NAME
       tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS
       #include 

       double tgamma(double x);
       float tgammaf(float x);
       long double tgammal(long double x);

       Link with -lm.

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

       tgamma(), tgammaf(), tgammal():
           XOPENSOURCE >= 600 || ISOC99SOURCE ||
           POSIXCSOURCE >= 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
       HUGEVAL, HUGEVALF, or HUGEVALL, 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
       HUGEVAL,  HUGEVALF, or HUGEVALL, respectively, with the same sign as
       the 0.

ERRORS
       See matherror(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
              (FEINVALID) 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 (FEDIVBYZERO) is raised.

       Range error: result overflow
              errno  is  set  to ERANGE.  An overflow floating-point exception
              (FEOVERFLOW) 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 (FEUNDERFLOW) is raised.

              errno is not set for this case.

VERSIONS
       These functions first appeared in glibc in version 2.1.

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

       ┌───────────────────────────────┬───────────────┬─────────┐
       │Interface                      │ Attribute     │ Value   │
       ├───────────────────────────────┼───────────────┼─────────┤
       │tgamma(), tgammaf(), tgammal() │ Thread safety │ MT-Safe │
       └───────────────────────────────┴───────────────┴─────────┘
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  incor‐
       rectly  produced  a  domain  error (errno set to EDOM and an FEINVALID
       exception raised), rather than a pole error.

SEE ALSO
       gamma(3), lgamma(3)

COLOPHON
       This page is part of release 3.53 of the Linux  man-pages  project.   A
       description  of  the project, and information about reporting bugs, can
       be found at http://www.kernel.org/doc/man-pages/.



GNU                               2010-09-20                         TGAMMA(3)