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" "libc math functions"
   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 nonpositive integers.
  25 For nonnegative 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. It had to be called "true gamma function"
  40 since there is already a function
  41 .IR gamma ()
  42 that returns something else.
  43 .SH ERRORS
  44 In order to check for errors, set
  45 .I errno
  46 to zero and call
  47 .I feclearexcept(FE_ALL_EXCEPT)
  48 before calling these functions. On return, if
  49 .I errno
  50 is non-zero or
  51 .I fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
  52 is non-zero, an error has occurred.
  53 .LP
  54 A range error occurs if x is too large.
  55 A pole error occurs if x is zero.
  56 A domain error (or a pole error) occurs if x is a negative integer.
  57 .SH "CONFORMING TO"
  58 C99.
  59 .SH "SEE ALSO"
  60 .BR gamma (3),
  61 .BR lgamma (3)