jn(3)

NAME#

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

LIBRARY#

Math library (libm, -lm)

SYNOPSIS#

#include <math.h>

double j0(double \nx\n);\n
\ndouble j1(double \nx\n);\n
\ndouble jn(int \nn\n, double \nx\n);

float j0f(float \nx\n);\n
\nfloat j1f(float \nx\n);\n
\nfloat jnf(int \nn\n, float \nx\n);

long double j0l(long double \nx\n);\n
\nlong double j1l(long double \nx\n);\n
\nlong double jnl(int \nn\n, long double \nx\n);

j0(), j1(), jn():

\n
    _XOPEN_SOURCE
\n
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
\n
        || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE

j0f(), j0l(), j1f(), j1l(), jnf(), jnl():

\n
    _XOPEN_SOURCE >= 600
\n
        || (_ISOC99_SOURCE && _XOPEN_SOURCE)
\n
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
\n
        || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE

DESCRIPTION#

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.

RETURN VALUE#

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.

ERRORS#

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).

ATTRIBUTES#

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

STANDARDS#

j0()

j1()

jn()

POSIX.1-2008.

Others:

BSD.

HISTORY#

j0()

j1()

jn()

SVr4, 4.3BSD, POSIX.1-2001, POSIX.1-2008.

Others:

BSD.

BUGS#

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.

SEE ALSO#

y0(3)