1 .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
2 .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
3 .\" <mtk.manpages@gmail.com>
5 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
7 .\" References consulted:
8 .\" Linux libc source code
9 .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
11 .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
12 .\" Modified 2002-08-25, aeb
13 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
14 .\" 2008-07-24, mtk, created this page, based on material from j0.3.
16 .TH Y0 3 (date) "Linux man-pages (unreleased)"
18 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
19 Bessel functions of the second kind
22 .RI ( libm ", " \-lm )
27 .BI "double y0(double " x );
28 .BI "double y1(double " x );
29 .BI "double yn(int " n ", double " x );
31 .BI "float y0f(float " x );
32 .BI "float y1f(float " x );
33 .BI "float ynf(int " n ", float " x );
35 .BI "long double y0l(long double " x );
36 .BI "long double y1l(long double " x );
37 .BI "long double ynl(int " n ", long double " x );
41 Feature Test Macro Requirements for glibc (see
42 .BR feature_test_macros (7)):
50 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
51 || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
62 || (_ISOC99_SOURCE && _XOPEN_SOURCE)
63 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
64 || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
71 functions return Bessel functions of
73 of the second kind of orders 0 and 1, respectively.
77 returns the Bessel function of
79 of the second kind of order
91 functions are versions that take and return
99 functions are versions that take and return
103 On success, these functions return the appropriate
104 Bessel value of the second kind for
109 is a NaN, a NaN is returned.
114 a domain error occurs,
115 and the functions return
121 (POSIX.1-2001 also allows a NaN return for this case.)
127 and the functions return
134 If the result underflows,
135 a range error occurs,
136 and the functions return 0.0
138 If the result overflows,
139 a range error occurs,
140 and the functions return
146 (POSIX.1-2001 also allows a 0.0 return for this case.)
150 for information on how to determine whether an error has occurred
151 when calling these functions.
153 The following errors can occur:
155 Domain error: \fIx\fP is negative
159 An invalid floating-point exception
163 Pole error: \fIx\fP is 0.0
164 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
165 .\" as a range error.
174 Range error: result underflow
175 .\" e.g., y0(1e33) on glibc 2.8/x86-32
181 exception is returned by
182 .\" This is intended behavior
183 .\" See http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
187 Range error: result overflow
188 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
193 An overflow floating-point exception
197 For an explanation of the terms used in this section, see
205 Interface Attribute Value
210 T} Thread safety MT-Safe
215 T} Thread safety MT-Safe
220 T} Thread safety MT-Safe
226 The functions returning
228 conform to SVr4, 4.3BSD,
229 POSIX.1-2001, POSIX.1-2008.
230 The others are nonstandard functions that also exist on the BSDs.
233 .\" http://sourceware.org/bugzilla/show_bug.cgi?id=6807
234 these functions misdiagnosed pole errors:
242 exception was raised.
245 .\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
248 for "range error: result underflow".
250 In glibc version 2.3.2 and earlier,
251 .\" Actually, 2.3.2 is the earliest test result I have; so yet
252 .\" to confirm if this error occurs only in 2.3.2.
253 these functions do not raise an invalid floating-point exception
255 when a domain error occurs.