diff options
Diffstat (limited to 'man3/tgamma.3')
| -rw-r--r-- | man3/tgamma.3 | 45 |
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 |