| .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk) |
| .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk |
| .\" <mtk.manpages@gmail.com> |
| .\" |
| .\" %%%LICENSE_START(VERBATIM) |
| .\" Permission is granted to make and distribute verbatim copies of this |
| .\" manual provided the copyright notice and this permission notice are |
| .\" preserved on all copies. |
| .\" |
| .\" Permission is granted to copy and distribute modified versions of this |
| .\" manual under the conditions for verbatim copying, provided that the |
| .\" entire resulting derived work is distributed under the terms of a |
| .\" permission notice identical to this one. |
| .\" |
| .\" Since the Linux kernel and libraries are constantly changing, this |
| .\" manual page may be incorrect or out-of-date. The author(s) assume no |
| .\" responsibility for errors or omissions, or for damages resulting from |
| .\" the use of the information contained herein. The author(s) may not |
| .\" have taken the same level of care in the production of this manual, |
| .\" which is licensed free of charge, as they might when working |
| .\" professionally. |
| .\" |
| .\" Formatted or processed versions of this manual, if unaccompanied by |
| .\" the source, must acknowledge the copyright and authors of this work. |
| .\" %%%LICENSE_END |
| .\" |
| .\" References consulted: |
| .\" Linux libc source code |
| .\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991) |
| .\" 386BSD man pages |
| .\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu) |
| .\" Modified 2002-08-25, aeb |
| .\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB |
| .\" 2008-07-24, mtk, moved yxx() material into separate y0.3 page |
| .\" |
| .TH J0 3 2016-03-15 "" "Linux Programmer's Manual" |
| .SH NAME |
| j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl \- |
| Bessel functions of the first kind |
| .SH SYNOPSIS |
| .nf |
| .B #include <math.h> |
| .sp |
| .fi |
| .BI "double j0(double " x ); |
| .br |
| .BI "double j1(double " x ); |
| .br |
| .BI "double jn(int " n ", double " x ); |
| .sp |
| .BI "float j0f(float " x ); |
| .br |
| .BI "float j1f(float " x ); |
| .br |
| .BI "float jnf(int " n ", float " x ); |
| .sp |
| .BI "long double j0l(long double " x ); |
| .br |
| .BI "long double j1l(long double " x ); |
| .br |
| .BI "long double jnl(int " n ", long double " x ); |
| .sp |
| Link with \fI\-lm\fP. |
| .sp |
| .in -4n |
| Feature Test Macro Requirements for glibc (see |
| .BR feature_test_macros (7)): |
| .in |
| .sp |
| .ad l |
| .BR j0 (), |
| .BR j1 (), |
| .BR jn (): |
| .RS 4 |
| _XOPEN_SOURCE |
| || /* Since glibc 2.19: */ _DEFAULT_SOURCE |
| || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE |
| .RE |
| .br |
| .BR j0f (), |
| .BR j0l (), |
| .BR j1f (), |
| .BR j1l (), |
| .BR jnf (), |
| .BR jnl (): |
| .RS 4 |
| _XOPEN_SOURCE \ >=\ 600 |
| || (_ISOC99_SOURCE && _XOPEN_SOURCE) |
| || /* Since glibc 2.19: */ _DEFAULT_SOURCE |
| || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE |
| .RE |
| .ad b |
| .SH DESCRIPTION |
| The |
| .BR j0 () |
| and |
| .BR j1 () |
| functions return Bessel functions of |
| .I x |
| of the first kind of orders 0 and 1, respectively. |
| The |
| .BR jn () |
| function |
| returns the Bessel function of |
| .I x |
| of the first kind of order |
| .IR n . |
| .PP |
| The |
| .BR j0f (), |
| .BR j1f (), |
| and |
| .BR jnf (), |
| functions are versions that take and return |
| .I float |
| values. |
| The |
| .BR j0l (), |
| .BR j1l (), |
| and |
| .BR jnl () |
| functions are versions that take and return |
| .I "long double" |
| values. |
| .SH RETURN VALUE |
| On success, these functions return the appropriate |
| Bessel value of the first kind for |
| .IR x . |
| |
| If |
| .I x |
| is a NaN, a NaN is returned. |
| |
| If |
| .I x |
| is too large in magnitude, |
| or the result underflows, |
| a range error occurs, |
| and the return value is 0. |
| .SH ERRORS |
| See |
| .BR math_error (7) |
| for information on how to determine whether an error has occurred |
| when calling these functions. |
| .PP |
| The following errors can occur: |
| .TP |
| Range error: result underflow, or \fIx\fP is too large in magnitude |
| .I errno |
| is set to |
| .BR ERANGE . |
| .\" An underflow floating-point exception |
| .\" .RB ( FE_UNDERFLOW ) |
| .\" is raised. |
| .PP |
| These functions do not raise exceptions for |
| .BR fetestexcept (3). |
| .\" FIXME . Is it intentional that these functions do not raise exceptions? |
| .\" e.g., j0(1.5e16) |
| .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6805 |
| .SH ATTRIBUTES |
| For an explanation of the terms used in this section, see |
| .BR attributes (7). |
| .TS |
| allbox; |
| lb lb lb |
| l l l. |
| Interface Attribute Value |
| T{ |
| .BR j0 (), |
| .BR j0f (), |
| .BR j0l () |
| T} Thread safety MT-Safe |
| T{ |
| .BR j1 (), |
| .BR j1f (), |
| .BR j1l () |
| T} Thread safety MT-Safe |
| T{ |
| .BR jn (), |
| .BR jnf (), |
| .BR jnl () |
| T} Thread safety MT-Safe |
| .TE |
| .SH CONFORMING TO |
| The functions returning |
| .I double |
| conform to SVr4, 4.3BSD, |
| POSIX.1-2001, and POSIX.1-2008. |
| The others are nonstandard functions that also exist on the BSDs. |
| .SH BUGS |
| There are errors of up to 2e\-16 in the values returned by |
| .BR j0 (), |
| .BR j1 () |
| and |
| .BR jn () |
| for values of |
| .I x |
| between \-8 and 8. |
| .SH SEE ALSO |
| .BR y0 (3) |