mirror of https://github.com/mkerrisk/man-pages
64 lines
1.7 KiB
Groff
64 lines
1.7 KiB
Groff
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\" Distributed under GPL
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.\" Based on glibc infopages
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.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
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.\" <kreutz@dbs.uni-hannover.de>
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.TH TGAMMA 3 2004-11-15 "GNU" "Linux Programmer's Manual"
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.SH NAME
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tgamma, tgammaf, tgammal \- true gamma function
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.SH SYNOPSIS
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.B #include <math.h>
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.sp
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.BI "double tgamma(double " x );
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.br
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.BI "float tgammaf(float " x );
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.br
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.BI "long double tgammal(long double " x );
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.sp
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Compile with \-std=c99; link with \-lm.
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.SH DESCRIPTION
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The Gamma function is defined by
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.sp
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Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
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.sp
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It is defined for every real number except for non-positive integers.
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For non-negative integral \fIm\fP one has
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.sp
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Gamma(m+1) = m!
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.sp
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and, more generally, for all \fIx\fP:
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.sp
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Gamma(x+1) = x * Gamma(x)
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.sp
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Furthermore, the following is valid for all values of \fIx\fP
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outside the poles:
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.sp
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Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
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.PP
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This function returns the value of the Gamma function for the
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argument \fIx\fP.
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It had to be called "true gamma function"
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since there is already a function
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.BR gamma (3)
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that returns something else.
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.SH ERRORS
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In order to check for errors, set
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.I errno
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to zero and call
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.I feclearexcept(FE_ALL_EXCEPT)
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before calling these functions.
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On return, if
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.I errno
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is non-zero or
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.I fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
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is non-zero, an error has occurred.
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.LP
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A range error occurs if x is too large.
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A pole error occurs if x is zero.
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A domain error (or a pole error) occurs if x is a negative integer.
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.SH "CONFORMING TO"
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C99.
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.SH "SEE ALSO"
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.BR gamma (3),
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.BR lgamma (3)
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