man3/j0.3

   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>
   4 .\"
   5 .\" SPDX-License-Identifier: Linux-man-pages-copyleft
   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
  13 .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
  14 .\" 2008-07-24, mtk, moved yxx() material into separate y0.3 page
  15 .\"
  16 .TH J0 3  2021-03-22 "" "Linux Programmer's Manual"
  17 .SH NAME
  18 j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl \-
  19 Bessel functions of the first kind
  20 .SH LIBRARY
  21 Math library
  22 .RI ( libm ", " \-lm )
  23 .SH SYNOPSIS
  24 .nf
  25 .B #include <math.h>
  26 .PP
  27 .BI "double j0(double " x );
  28 .BI "double j1(double " x );
  29 .BI "double jn(int " n ", double " x );
  30 .PP
  31 .BI "float j0f(float " x );
  32 .BI "float j1f(float " x );
  33 .BI "float jnf(int " n ", float " x );
  34 .PP
  35 .BI "long double j0l(long double " x );
  36 .BI "long double j1l(long double " x );
  37 .BI "long double jnl(int " n ", long double " x );
  38 .fi
  39 .PP
  40 .RS -4
  41 Feature Test Macro Requirements for glibc (see
  42 .BR feature_test_macros (7)):
  43 .RE
  44 .PP
  45 .BR j0 (),
  46 .BR j1 (),
  47 .BR jn ():
  48 .nf
  49     _XOPEN_SOURCE
  50         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  51         || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
  52 .fi
  53 .PP
  54 .BR j0f (),
  55 .BR j0l (),
  56 .BR j1f (),
  57 .BR j1l (),
  58 .BR jnf (),
  59 .BR jnl ():
  60 .nf
  61     _XOPEN_SOURCE >= 600
  62         || (_ISOC99_SOURCE && _XOPEN_SOURCE)
  63         || /* Since glibc 2.19: */ _DEFAULT_SOURCE
  64         || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
  65 .fi
  66 .SH DESCRIPTION
  67 The
  68 .BR j0 ()
  69 and
  70 .BR j1 ()
  71 functions return Bessel functions of
  72 .I x
  73 of the first kind of orders 0 and 1, respectively.
  74 The
  75 .BR jn ()
  76 function
  77 returns the Bessel function of
  78 .I x
  79 of the first kind of order
  80 .IR n .
  81 .PP
  82 The
  83 .BR j0f (),
  84 .BR j1f (),
  85 and
  86 .BR jnf (),
  87 functions are versions that take and return
  88 .I float
  89 values.
  90 The
  91 .BR j0l (),
  92 .BR j1l (),
  93 and
  94 .BR jnl ()
  95 functions are versions that take and return
  96 .I "long double"
  97 values.
  98 .SH RETURN VALUE
  99 On success, these functions return the appropriate
 100 Bessel value of the first kind for
 101 .IR x .
 102 .PP
 103 If
 104 .I x
 105 is a NaN, a NaN is returned.
 106 .PP
 107 If
 108 .I x
 109 is too large in magnitude,
 110 or the result underflows,
 111 a range error occurs,
 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 .
 125 .PP
 126 These functions do not raise exceptions for
 127 .BR fetestexcept (3).
 128 .\" e.g., j0(1.5e16)
 129 .\" This is intentional.
 130 .\" See http://sources.redhat.com/bugzilla/show_bug.cgi?id=6805
 131 .SH ATTRIBUTES
 132 For an explanation of the terms used in this section, see
 133 .BR attributes (7).
 134 .ad l
 135 .nh
 136 .TS
 137 allbox;
 138 lbx lb lb
 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
 157 .hy
 158 .ad
 159 .sp 1
 160 .SH CONFORMING TO
 161 The functions returning
 162 .I double
 163 conform to SVr4, 4.3BSD,
 164 POSIX.1-2001, and POSIX.1-2008.
 165 The others are nonstandard functions that also exist on the BSDs.
 166 .SH BUGS
 167 There are errors of up to 2e\-16 in the values returned by
 168 .BR j0 (),
 169 .BR j1 (),
 170 and
 171 .BR jn ()
 172 for values of
 173 .I x
 174 between \-8 and 8.
 175 .SH SEE ALSO
 176 .BR y0 (3)