tgamma man page on Archlinux

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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

       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.

       C99, POSIX.1-2001.

       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).

       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  FE_INVALID
       exception raised), rather than a pole error.

       gamma(3), lgamma(3)

       This  page  is  part of release 3.65 of the Linux man-pages project.  A
       description of the project, and information about reporting  bugs,  can
       be found at

GNU				  2010-09-20			     TGAMMA(3)

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