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 .\" Permission is granted to make and distribute verbatim copies of this
6 .\" manual provided the copyright notice and this permission notice are
7 .\" preserved on all copies.
9 .\" Permission is granted to copy and distribute modified versions of this
10 .\" manual under the conditions for verbatim copying, provided that the
11 .\" entire resulting derived work is distributed under the terms of a
12 .\" permission notice identical to this one.
14 .\" Since the Linux kernel and libraries are constantly changing, this
15 .\" manual page may be incorrect or out-of-date. The author(s) assume no
16 .\" responsibility for errors or omissions, or for damages resulting from
17 .\" the use of the information contained herein. The author(s) may not
18 .\" have taken the same level of care in the production of this manual,
19 .\" which is licensed free of charge, as they might when working
22 .\" Formatted or processed versions of this manual, if unaccompanied by
23 .\" the source, must acknowledge the copyright and authors of this work.
25 .\" References consulted:
26 .\" Linux libc source code
27 .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
29 .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
30 .\" Modified 2002-08-25, aeb
31 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
32 .\" 2008-07-24, mtk, created this page, based on material from j0.3.
34 .TH Y0 3 2008-08-10 "" "Linux Programmer's Manual"
36 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
37 Bessel functions of the second kind
42 .BI "double y0(double " x );
44 .BI "double y1(double " x );
46 .BI "double yn(int " n ", double " x );
48 .BI "float y0f(float " x );
50 .BI "float y1f(float " x );
52 .BI "float ynf(int " n ", float " x );
54 .BI "long double y0l(long double " x );
56 .BI "long double y1l(long double " x );
58 .BI "long double ynl(int " n ", long double " x );
64 Feature Test Macro Requirements for glibc (see
65 .BR feature_test_macros (7)):
72 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
80 _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE\ >=\ 600
81 .\" Also seems to work: -std=c99 -D_XOPEN_SOURCE
89 functions return Bessel functions of \fIx\fP
90 of the second kind of orders 0 and 1, respectively.
94 returns the Bessel function of \fIx\fP of the second kind of order \fIn\fP.
96 The value of \fIx\fP must be positive.
102 etc. functions are versions that take and return
106 values, respectively.
108 On success, these functions return the appropriate
109 Bessel value of the second kind for
114 is a NaN, a NaN is returned.
119 a domain error occurs,
120 and the functions return
126 (POSIX.1-2001 also allows a NaN return for this case.)
132 and the functions return
139 If the result underflows,
140 a range error occurs,
141 and the functions return 0.0
143 If the result overflows,
144 a range error occurs,
145 and the functions return
151 (POSIX.1-2001 also allows a 0.0 return for this case.)
155 for information on how to determine whether an error has occurred
156 when calling these functions.
158 The following errors can occur:
160 Domain error: \fIx\fP is negative
164 An invalid floating-point exception
168 Pole error: \fIx\fP is 0.0
169 .\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
170 .\" as a range error.
173 .\" FIXME . y0(0.0) gives EDOM
178 exception is returned by
181 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
183 Range error: result underflow
184 .\" e.g., y0(1e33) on glibc 2.8/x86-32
188 .\" An underflow floating-point exception
189 .\" .RB ( FE_UNDERFLOW )
191 .\" FIXME . Is it intentional that these functions do not use FE_*?
192 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806
195 exception is returned by
199 Range error: result overflow
200 .\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
205 is not set for this case.
206 .\" FIXME . Is it intentional that errno is not set?
207 .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808
208 An overflow floating-point exception
212 The functions returning
214 conform to SVr4, 4.3BSD,
216 The others are non-standard functions that also exist on the BSDs.
218 On a pole error, these functions set
224 as POSIX.1-2004 requires.
226 .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807
228 In glibc version 2.3.2 and earlier,
229 .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet
230 .\" to confirm if this error occurs only in 2.3.2.
231 these functions do not raise an invalid floating-point exception
233 when a domain error occurs.