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fea681da | 1 | .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk) |
8f6f581d MK |
2 | .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk |
3 | .\" <mtk.manpages@gmail.com> | |
fea681da | 4 | .\" |
5fbde956 | 5 | .\" SPDX-License-Identifier: Linux-man-pages-copyleft |
fea681da MK |
6 | .\" |
7 | .\" References consulted: | |
8 | .\" Linux libc source code | |
9 | .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991) | |
10 | .\" 386BSD man pages | |
11 | .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu) | |
12 | .\" Modified 2002-08-25, aeb | |
b4528020 | 13 | .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB |
8f6f581d | 14 | .\" 2008-07-24, mtk, moved yxx() material into separate y0.3 page |
fea681da | 15 | .\" |
1ae6b2c7 | 16 | .TH J0 3 2021-03-22 GNU "Linux Programmer's Manual" |
fea681da | 17 | .SH NAME |
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18 | j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl \- |
19 | Bessel functions of the first kind | |
bd8c9d7c AC |
20 | .SH LIBRARY |
21 | Math library | |
8fc3b2cf | 22 | .RI ( libm ", " \-lm ) |
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23 | .SH SYNOPSIS |
24 | .nf | |
25 | .B #include <math.h> | |
68e4db0a | 26 | .PP |
fea681da | 27 | .BI "double j0(double " x ); |
fea681da | 28 | .BI "double j1(double " x ); |
fea681da | 29 | .BI "double jn(int " n ", double " x ); |
68e4db0a | 30 | .PP |
fea681da | 31 | .BI "float j0f(float " x ); |
fea681da | 32 | .BI "float j1f(float " x ); |
fea681da | 33 | .BI "float jnf(int " n ", float " x ); |
68e4db0a | 34 | .PP |
fea681da | 35 | .BI "long double j0l(long double " x ); |
fea681da | 36 | .BI "long double j1l(long double " x ); |
fea681da | 37 | .BI "long double jnl(int " n ", long double " x ); |
a1048f8e | 38 | .fi |
68e4db0a | 39 | .PP |
d39ad78f | 40 | .RS -4 |
cc4615cc MK |
41 | Feature Test Macro Requirements for glibc (see |
42 | .BR feature_test_macros (7)): | |
d39ad78f | 43 | .RE |
68e4db0a | 44 | .PP |
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45 | .BR j0 (), |
46 | .BR j1 (), | |
64425118 | 47 | .BR jn (): |
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48 | .nf |
49 | _XOPEN_SOURCE | |
50 | || /* Since glibc 2.19: */ _DEFAULT_SOURCE | |
51 | || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE | |
52 | .fi | |
98c9347c | 53 | .PP |
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54 | .BR j0f (), |
55 | .BR j0l (), | |
56 | .BR j1f (), | |
57 | .BR j1l (), | |
58 | .BR jnf (), | |
64425118 | 59 | .BR jnl (): |
9d2adbae | 60 | .nf |
5c10d2c5 | 61 | _XOPEN_SOURCE >= 600 |
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62 | || (_ISOC99_SOURCE && _XOPEN_SOURCE) |
63 | || /* Since glibc 2.19: */ _DEFAULT_SOURCE | |
64 | || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE | |
65 | .fi | |
fea681da | 66 | .SH DESCRIPTION |
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67 | The |
68 | .BR j0 () | |
69 | and | |
70 | .BR j1 () | |
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71 | functions return Bessel functions of |
72 | .I x | |
c13182ef | 73 | of the first kind of orders 0 and 1, respectively. |
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74 | The |
75 | .BR jn () | |
76 | function | |
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77 | returns the Bessel function of |
78 | .I x | |
79 | of the first kind of order | |
80 | .IR n . | |
fea681da | 81 | .PP |
60a90ecd | 82 | The |
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83 | .BR j0f (), |
84 | .BR j1f (), | |
85 | and | |
86 | .BR jnf (), | |
87 | functions are versions that take and return | |
c13182ef | 88 | .I float |
4e0344e4 MK |
89 | values. |
90 | The | |
91 | .BR j0l (), | |
92 | .BR j1l (), | |
c13182ef | 93 | and |
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94 | .BR jnl () |
95 | functions are versions that take and return | |
68e1685c | 96 | .I "long double" |
4e0344e4 | 97 | values. |
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98 | .SH RETURN VALUE |
99 | On success, these functions return the appropriate | |
100 | Bessel value of the first kind for | |
101 | .IR x . | |
847e0d88 | 102 | .PP |
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103 | If |
104 | .I x | |
105 | is a NaN, a NaN is returned. | |
847e0d88 | 106 | .PP |
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107 | If |
108 | .I x | |
109 | is too large in magnitude, | |
110 | or the result underflows, | |
efe294cb | 111 | a range error occurs, |
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112 | and the return value is 0. |
113 | .SH ERRORS | |
114 | See | |
115 | .BR math_error (7) | |
116 | for information on how to determine whether an error has occurred | |
117 | when calling these functions. | |
118 | .PP | |
119 | The following errors can occur: | |
120 | .TP | |
121 | Range error: result underflow, or \fIx\fP is too large in magnitude | |
122 | .I errno | |
123 | is set to | |
124 | .BR ERANGE . | |
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125 | .PP |
126 | These functions do not raise exceptions for | |
127 | .BR fetestexcept (3). | |
8f6f581d | 128 | .\" e.g., j0(1.5e16) |
84828d04 MK |
129 | .\" This is intentional. |
130 | .\" See http://sources.redhat.com/bugzilla/show_bug.cgi?id=6805 | |
97944d60 MS |
131 | .SH ATTRIBUTES |
132 | For an explanation of the terms used in this section, see | |
133 | .BR attributes (7). | |
c466875e MK |
134 | .ad l |
135 | .nh | |
97944d60 MS |
136 | .TS |
137 | allbox; | |
c466875e | 138 | lbx lb lb |
97944d60 MS |
139 | l l l. |
140 | Interface Attribute Value | |
141 | T{ | |
142 | .BR j0 (), | |
143 | .BR j0f (), | |
144 | .BR j0l () | |
145 | T} Thread safety MT-Safe | |
146 | T{ | |
147 | .BR j1 (), | |
148 | .BR j1f (), | |
149 | .BR j1l () | |
150 | T} Thread safety MT-Safe | |
151 | T{ | |
152 | .BR jn (), | |
153 | .BR jnf (), | |
154 | .BR jnl () | |
155 | T} Thread safety MT-Safe | |
156 | .TE | |
c466875e MK |
157 | .hy |
158 | .ad | |
159 | .sp 1 | |
47297adb | 160 | .SH CONFORMING TO |
c13182ef MK |
161 | The functions returning |
162 | .I double | |
68e1685c | 163 | conform to SVr4, 4.3BSD, |
9a0216ac | 164 | POSIX.1-2001, and POSIX.1-2008. |
c8f2dd47 | 165 | The others are nonstandard functions that also exist on the BSDs. |
fea681da | 166 | .SH BUGS |
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167 | There are errors of up to 2e\-16 in the values returned by |
168 | .BR j0 (), | |
d556548b | 169 | .BR j1 (), |
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170 | and |
171 | .BR jn () | |
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172 | for values of |
173 | .I x | |
174 | between \-8 and 8. | |
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175 | .SH SEE ALSO |
176 | .BR y0 (3) |