man3/tgamma.3

   1 .\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
   2 .\" Distributed under GPL
   3 .\" Based on glibc infopages
   4 .\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
   5 .\"      <kreutz@dbs.uni-hannover.de>
   6 .TH TGAMMA 3 2004-11-15 "GNU" "Linux Programmer's Manual"
   7 .SH NAME
   8 tgamma, tgammaf, tgammal \- true gamma function
   9 .SH SYNOPSIS
  10 .B #include <math.h>
  11 .sp
  12 .BI "double tgamma(double " x );
  13 .br
  14 .BI "float tgammaf(float " x );
  15 .br
  16 .BI "long double tgammal(long double " x );
  17 .sp
  18 Compile with \-std=c99; link with \-lm.
  19 .SH DESCRIPTION
  20 The Gamma function is defined by
  21 .sp
  22  Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
  23 .sp
  24 It is defined for every real number except for non-positive integers.
  25 For non-negative integral \fIm\fP one has
  26 .sp
  27  Gamma(m+1) = m!
  28 .sp
  29 and, more generally, for all \fIx\fP:
  30 .sp
  31  Gamma(x+1) = x * Gamma(x)
  32 .sp
  33 Furthermore, the following is valid for all values of \fIx\fP
  34 outside the poles:
  35 .sp
  36  Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
  37 .PP
  38 This function returns the value of the Gamma function for the
  39 argument \fIx\fP.
  40 It had to be called "true gamma function"
  41 since there is already a function
  42 .BR gamma (3)
  43 that returns something else.
  44 .SH ERRORS
  45 In order to check for errors, set
  46 .I errno
  47 to zero and call
  48 .I feclearexcept(FE_ALL_EXCEPT)
  49 before calling these functions.
  50 On return, if
  51 .I errno
  52 is non-zero or
  53 .I fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
  54 is non-zero, an error has occurred.
  55 .LP
  56 A range error occurs if x is too large.
  57 A pole error occurs if x is zero.
  58 A domain error (or a pole error) occurs if x is a negative integer.
  59 .SH "CONFORMING TO"
  60 C99.
  61 .SH "SEE ALSO"
  62 .BR gamma (3),
  63 .BR lgamma (3)