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 .\" %%%LICENSE_START(VERBATIM)
6 .\" Permission is granted to make and distribute verbatim copies of this
7 .\" manual provided the copyright notice and this permission notice are
8 .\" preserved on all copies.
10 .\" Permission is granted to copy and distribute modified versions of this
11 .\" manual under the conditions for verbatim copying, provided that the
12 .\" entire resulting derived work is distributed under the terms of a
13 .\" permission notice identical to this one.
15 .\" Since the Linux kernel and libraries are constantly changing, this
16 .\" manual page may be incorrect or out-of-date. The author(s) assume no
17 .\" responsibility for errors or omissions, or for damages resulting from
18 .\" the use of the information contained herein. The author(s) may not
19 .\" have taken the same level of care in the production of this manual,
20 .\" which is licensed free of charge, as they might when working
23 .\" Formatted or processed versions of this manual, if unaccompanied by
24 .\" the source, must acknowledge the copyright and authors of this work.
27 .\" References consulted:
28 .\" Linux libc source code
29 .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
31 .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
32 .\" Modified 2002-08-25, aeb
33 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
34 .\" 2008-07-24, mtk, created this page, based on material from j0.3.
36 .TH Y0 3 2017-09-15 "" "Linux Programmer's Manual"
38 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
39 Bessel functions of the second kind
44 .BI "double y0(double " x );
45 .BI "double y1(double " x );
46 .BI "double yn(int " n ", double " x );
48 .BI "float y0f(float " x );
49 .BI "float y1f(float " x );
50 .BI "float ynf(int " n ", float " x );
52 .BI "long double y0l(long double " x );
53 .BI "long double y1l(long double " x );
54 .BI "long double ynl(int " n ", long double " x );
60 Feature Test Macro Requirements for glibc (see
61 .BR feature_test_macros (7)):
70 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
71 || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
81 _XOPEN_SOURCE \ >=\ 600
82 || (_ISOC99_SOURCE && _XOPEN_SOURCE)
83 || /* Since glibc 2.19: */ _DEFAULT_SOURCE
84 || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
93 functions return Bessel functions of
95 of the second kind of orders 0 and 1, respectively.
99 returns the Bessel function of
101 of the second kind of order
113 functions are versions that take and return
121 functions are versions that take and return
125 On success, these functions return the appropriate
126 Bessel value of the second kind for
131 is a NaN, a NaN is returned.
136 a domain error occurs,
137 and the functions return
143 (POSIX.1-2001 also allows a NaN return for this case.)
149 and the functions return
156 If the result underflows,
157 a range error occurs,
158 and the functions return 0.0
160 If the result overflows,
161 a range error occurs,
162 and the functions return
168 (POSIX.1-2001 also allows a 0.0 return for this case.)
172 for information on how to determine whether an error has occurred
173 when calling these functions.
175 The following errors can occur:
177 Domain error: \fIx\fP is negative
181 An invalid floating-point exception
185 Pole error: \fIx\fP is 0.0
186 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
187 .\" as a range error.
190 .\" FIXME . y0(0.0) gives EDOM
195 exception is returned by
198 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
200 Range error: result underflow
201 .\" e.g., y0(1e33) on glibc 2.8/x86-32
205 .\" An underflow floating-point exception
206 .\" .RB ( FE_UNDERFLOW )
208 .\" FIXME . Is it intentional that these functions do not use FE_*?
209 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
212 exception is returned by
216 Range error: result overflow
217 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
222 is not set for this case.
223 .\" FIXME . Is it intentional that errno is not set?
224 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
225 An overflow floating-point exception
229 For an explanation of the terms used in this section, see
235 Interface Attribute Value
240 T} Thread safety MT-Safe
245 T} Thread safety MT-Safe
250 T} Thread safety MT-Safe
253 The functions returning
255 conform to SVr4, 4.3BSD,
256 POSIX.1-2001, POSIX.1-2008.
257 The others are nonstandard functions that also exist on the BSDs.
259 On a pole error, these functions set
265 as POSIX.1-2004 requires.
267 .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
269 In glibc version 2.3.2 and earlier,
270 .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet
271 .\" to confirm if this error occurs only in 2.3.2.
272 these functions do not raise an invalid floating-point exception
274 when a domain error occurs.