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
   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,
          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
   attributes(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
   already  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
   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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   description  of  the project, information about reporting bugs, and the
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