2 .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
3 .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
4 .\" <mtk.manpages@gmail.com>
6 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
8 .\" References consulted:
9 .\" Linux libc source code
10 .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
12 .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
13 .\" Modified 2002-08-25, aeb
14 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
15 .\" 2008-07-24, mtk, created this page, based on material from j0.3.
17 .TH y0 3 (date) "Linux man-pages (unreleased)"
19 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
20 Bessel functions of the second kind
23 .RI ( libm ", " \-lm )
28 .BI "double y0(double " x );
29 .BI "double y1(double " x );
30 .BI "double yn(int " n ", double " x );
32 .BI "float y0f(float " x );
33 .BI "float y1f(float " x );
34 .BI "float ynf(int " n ", float " x );
36 .BI "long double y0l(long double " x );
37 .BI "long double y1l(long double " x );
38 .BI "long double ynl(int " n ", long double " x );
42 Feature Test Macro Requirements for glibc (see
43 .BR feature_test_macros (7)):
51 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
52 || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
63 || (_ISOC99_SOURCE && _XOPEN_SOURCE)
64 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
65 || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
72 functions return Bessel functions of
74 of the second kind of orders 0 and 1, respectively.
78 returns the Bessel function of
80 of the second kind of order
92 functions are versions that take and return
100 functions are versions that take and return
104 On success, these functions return the appropriate
105 Bessel value of the second kind for
110 is a NaN, a NaN is returned.
115 a domain error occurs,
116 and the functions return
122 (POSIX.1-2001 also allows a NaN return for this case.)
128 and the functions return
135 If the result underflows,
136 a range error occurs,
137 and the functions return 0.0
139 If the result overflows,
140 a range error occurs,
141 and the functions return
147 (POSIX.1-2001 also allows a 0.0 return for this case.)
151 for information on how to determine whether an error has occurred
152 when calling these functions.
154 The following errors can occur:
156 Domain error: \fIx\fP is negative
160 An invalid floating-point exception
164 Pole error: \fIx\fP is 0.0
165 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
166 .\" as a range error.
175 Range error: result underflow
176 .\" e.g., y0(1e33) on glibc 2.8/x86-32
182 exception is returned by
183 .\" This is intended behavior
184 .\" See https://www.sourceware.org/bugzilla/show_bug.cgi?id=6806
188 Range error: result overflow
189 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
194 An overflow floating-point exception
198 For an explanation of the terms used in this section, see
206 Interface Attribute Value
211 T} Thread safety MT-Safe
216 T} Thread safety MT-Safe
221 T} Thread safety MT-Safe
251 .\" http://sourceware.org/bugzilla/show_bug.cgi?id=6807
252 these functions misdiagnosed pole errors:
260 exception was raised.
263 .\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6808
266 for "range error: result underflow".
268 In glibc 2.3.2 and earlier,
269 .\" Actually, 2.3.2 is the earliest test result I have; so yet
270 .\" to confirm if this error occurs only in glibc 2.3.2.
271 these functions do not raise an invalid floating-point exception
273 when a domain error occurs.