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():
20           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
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DESCRIPTION

23       These functions calculate the Gamma function of x.
24
25       The Gamma function is defined by
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27              Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
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29       It  is  defined  for every real number except for nonpositive integers.
30       For nonnegative integral m one has
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32              Gamma(m+1) = m!
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34       and, more generally, for all x:
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36              Gamma(x+1) = x * Gamma(x)
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38       Furthermore, the following is valid for all values  of  x  outside  the
39       poles:
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41              Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
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RETURN VALUE

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

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

90       These functions first appeared in glibc in version 2.1.
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ATTRIBUTES

93       For  an  explanation  of  the  terms  used  in  this  section,  see at‐
94       tributes(7).
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96       ┌────────────────────────────────────────────┬───────────────┬─────────┐
97       │Interface                                   │ Attribute     │ Value   │
98       ├────────────────────────────────────────────┼───────────────┼─────────┤
99       │tgamma(), tgammaf(), tgammal()              │ Thread safety │ MT-Safe │
100       └────────────────────────────────────────────┴───────────────┴─────────┘
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CONFORMING TO

103       C99, POSIX.1-2001, POSIX.1-2008.
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NOTES

106       This function had to be called "true gamma function" since there is al‐
107       ready a function gamma(3) that returns something else (see gamma(3) for
108       details).
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BUGS

111       Before version 2.18, the glibc implementation of  these  functions  did
112       not set errno to EDOM when x is negative infinity.
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114       Before  glibc 2.19, the glibc implementation of these functions did not
115       set errno to ERANGE on an underflow range error.
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117       In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrect‐
118       ly  produced a domain error (errno set to EDOM and an FE_INVALID excep‐
119       tion raised), rather than a pole error.
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COLOPHON

125       This page is part of release 5.13 of the Linux  man-pages  project.   A
126       description  of  the project, information about reporting bugs, and the
127       latest    version    of    this    page,    can     be     found     at
128       https://www.kernel.org/doc/man-pages/.
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132GNU                               2021-03-22                         TGAMMA(3)