j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl — Bessel functions of the first kind


#include <math.h>
double j0( double x);
double j1( double x);
double jn( int n,
  double x);
float j0f( float x);
float j1f( float x);
float jnf( int n,
  float x);
long double j0l( long double x);
long double j1l( long double x);
long double jnl( int n,
  long double x);
[Note] Note
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
j0(), j1(), jn():
_XOPEN_SOURCE || /* Since glibc 2.19:
*/ _DEFAULT_SOURCE || /* Glibc <= 2.19:
j0f(), j0l(), j1f(), j1l(), jnf(), jnl():
_XOPEN_SOURCE >= 600 || (_ISOC99_SOURCE && _XOPEN_SOURCE) || /* Since glibc 2.19:
*/ _DEFAULT_SOURCE || /* Glibc <= 2.19:
[Note] Note

Link with −lm.


The j0() and j1() functions return Bessel functions of x of the first kind of orders 0 and 1, respectively. The jn() function returns the Bessel function of x of the first kind of order n.

The j0f(), j1f(), and jnf(), functions are versions that take and return float values. The j0l(), j1l(), and jnl() functions are versions that take and return long double values.


On success, these functions return the appropriate Bessel value of the first kind for x.

If x is a NaN, a NaN is returned.

If x is too large in magnitude, or the result underflows, a range error occurs, and the return value is 0.


See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

Range error: result underflow, or x is too large in magnitude

errno is set to ERANGE.

These functions do not raise exceptions for fetestexcept(3).


For an explanation of the terms used in this section, see attributes(7).

Interface Attribute Value
j0(), j0f(), j0l() Thread safety MT-Safe
j1(), j1f(), j1l() Thread safety MT-Safe
jn(), jnf(), jnl() Thread safety MT-Safe


The functions returning double conform to SVr4, 4.3BSD, POSIX.1-2001, and POSIX.1-2008. The others are nonstandard functions that also exist on the BSDs.


There are errors of up to 2e−16 in the values returned by j0(), j1(), and jn() for values of x between −8 and 8.




This page is part of release 5.11 of the Linux man-pages project. A description of the project, information about reporting bugs, and the latest version of this page, can be found at−pages/.

  Copyright 1993 David Metcalfe (
and Copyright 2008, Linux Foundation, written by Michael Kerrisk

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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 (
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