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authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-15 19:41:07 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-15 19:41:07 +0000
commit3af6d22bb3850ab2bac67287e3a3d3b0e32868e5 (patch)
tree3ee7a3ec64525911fa865bb984c86d997d855527 /man3/tgamma.3
parentAdding debian version 6.05.01-1. (diff)
downloadmanpages-3af6d22bb3850ab2bac67287e3a3d3b0e32868e5.tar.xz
manpages-3af6d22bb3850ab2bac67287e3a3d3b0e32868e5.zip
Merging upstream version 6.7.
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'man3/tgamma.3')
-rw-r--r--man3/tgamma.345
1 files changed, 22 insertions, 23 deletions
diff --git a/man3/tgamma.3 b/man3/tgamma.3
index d2c5969..e62069c 100644
--- a/man3/tgamma.3
+++ b/man3/tgamma.3
@@ -9,7 +9,7 @@
.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
.\" <kreutz@dbs.uni-hannover.de>
.\"
-.TH tgamma 3 2023-07-20 "Linux man-pages 6.05.01"
+.TH tgamma 3 2023-10-31 "Linux man-pages 6.7"
.SH NAME
tgamma, tgammaf, tgammal \- true gamma function
.SH LIBRARY
@@ -18,17 +18,17 @@ Math library
.SH SYNOPSIS
.nf
.B #include <math.h>
-.PP
+.P
.BI "double tgamma(double " x );
.BI "float tgammaf(float " x );
.BI "long double tgammal(long double " x );
.fi
-.PP
+.P
.RS -4
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.RE
-.PP
+.P
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ():
@@ -38,53 +38,53 @@ Feature Test Macro Requirements for glibc (see
.SH DESCRIPTION
These functions calculate the Gamma function of
.IR x .
-.PP
+.P
The Gamma function is defined by
-.PP
+.P
.RS
Gamma(x) = integral from 0 to infinity of t\[ha](x\-1) e\[ha]\-t dt
.RE
-.PP
+.P
It is defined for every real number except for nonpositive integers.
For nonnegative integral
.I m
one has
-.PP
+.P
.RS
Gamma(m+1) = m!
.RE
-.PP
+.P
and, more generally, for all
.IR x :
-.PP
+.P
.RS
Gamma(x+1) = x * Gamma(x)
.RE
-.PP
+.P
Furthermore, the following is valid for all values of
.I x
outside the poles:
-.PP
+.P
.RS
Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
.RE
.SH RETURN VALUE
On success, these functions return Gamma(x).
-.PP
+.P
If
.I x
is a NaN, a NaN is returned.
-.PP
+.P
If
.I x
is positive infinity, positive infinity is returned.
-.PP
+.P
If
.I x
is a negative integer, or is negative infinity,
a domain error occurs,
and a NaN is returned.
-.PP
+.P
If the result overflows,
a range error occurs,
and the functions return
@@ -93,11 +93,11 @@ and the functions return
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
-.PP
+.P
If the result underflows,
a range error occurs,
and the functions return 0, with the correct mathematical sign.
-.PP
+.P
If
.I x
is \-0 or +0,
@@ -113,7 +113,7 @@ See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
-.PP
+.P
The following errors can occur:
.TP
Domain error: \fIx\fP is a negative integer, or negative infinity
@@ -139,7 +139,7 @@ is set to
An overflow floating-point exception
.RB ( FE_OVERFLOW )
is raised.
-.PP
+.P
glibc also gives the following error which is not specified
in C99 or POSIX.1-2001.
.TP
@@ -172,7 +172,6 @@ T{
.BR tgammal ()
T} Thread safety MT-Safe
.TE
-.sp 1
.SH STANDARDS
C11, POSIX.1-2008.
.SH HISTORY
@@ -194,7 +193,7 @@ to
when
.I x
is negative infinity.
-.PP
+.P
Before glibc 2.19,
.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6810
the glibc implementation of these functions did not set
@@ -202,7 +201,7 @@ the glibc implementation of these functions did not set
to
.B ERANGE
on an underflow range error.
-.PP
+.P
.\"
In glibc versions 2.3.3 and earlier,
an argument of +0 or \-0 incorrectly produced a domain error