tgamma(3)

1TGAMMA(3)                  Linux Programmer's Manual                 TGAMMA(3)
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NAME

6       tgamma, tgammaf, tgammal - true gamma function
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SYNOPSIS

9       #include <math.h>
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11       double tgamma(double x);
12       float tgammaf(float x);
13       long double tgammal(long double x);
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15       Link with -lm.
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17   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
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19       tgamma(), tgammaf(), tgammal(): _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE;
20       or cc -std=c99
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DESCRIPTION

23       The Gamma function is defined by
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25           Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
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27       It is defined for every real number except for  non-positive  integers.
28       For non-negative integral m one has
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30           Gamma(m+1) = m!
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32       and, more generally, for all x:
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34           Gamma(x+1) = x * Gamma(x)
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36       Furthermore,  the  following  is  valid for all values of x outside the
37       poles:
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39           Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
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RETURN VALUE

42       On success, these functions return Gamma(x).
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44       If x is a NaN, a NaN is returned.
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46       If x is positive infinity, positive infinity is returned.
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48       If x is a negative integer, or is negative  infinity,  a  domain  error
49       occurs, and a NaN is returned.
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51       If the result overflows, a range error occurs, and the functions return
52       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct math‐
53       ematical sign.
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55       If  the  result  underflows,  a  range  error occurs, and the functions
56       return 0, with the correct mathematical sign.
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58       If x is -0 or +0,  a  pole  error  occurs,  and  the  functions  return
59       HUGE_VAL,  HUGE_VALF, or HUGE_VALL, respectively, with the same sign as
60       the 0.
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ERRORS

63       See math_error(7) for information on how to determine whether an  error
64       has occurred when calling these functions.
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66       The following errors can occur:
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68       Domain error: x is a negative integer, or negative infinity
69              errno  is  set  to  EDOM.   An  invalid floating-point exception
70              (FE_INVALID) is raised (but see BUGS).
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72       Pole error: x is +0 or -0
73              errno is set to ERANGE.  A divide-by-zero floating-point  excep‐
74              tion (FE_DIVBYZERO) is raised.
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76       Range error: result overflow
77              errno  is  set  to ERANGE.  An overflow floating-point exception
78              (FE_OVERFLOW) is raised.
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80       glibc also gives the following error which is not specified in  C99  or
81       POSIX.1-2001.
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83       Range error: result underflow
84              An underflow floating-point exception (FE_UNDERFLOW) is raised.
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86              errno is not set for this case.
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VERSIONS

89       These functions first appeared in glibc in version 2.1.
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CONFORMING TO

92       C99, POSIX.1-2001.
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NOTES

95       This  function  had  to  be called "true gamma function" since there is
96       already a function gamma(3) that returns something else  (see  gamma(3)
97       for details).
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BUGS

100       If x is negative infinity, errno is not set (it should be set to EDOM).
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102       In  glibc  versions  2.3.3  and earlier, an argument of +0 or -0 incor‐
103       rectly produced a domain error (errno set to  EDOM  and  an  FE_INVALID
104       exception raised), rather than a pole error.
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COLOPHON

110       This  page  is  part of release 3.22 of the Linux man-pages project.  A
111       description of the project, and information about reporting  bugs,  can
112       be found at http://www.kernel.org/doc/man-pages/.
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116GNU                               2008-08-11                         TGAMMA(3)