# JN

## Purpose:

Evaluates the Bessel function of the first
kind for integer orders.

## Syntax:

JN(z, order)

z |
- |
A series or scalar. |

order |
- |
Optional. An integer, the order. Defaults
to 0. |

## Returns:

A real, series, or table the value of
J_{n}(z)
where z is the input and n is
the integer order.

## Example:

jn(3.0, 1)

returns the scalar 0.3390, the value of
J_{1}(3).

## Example:

z = 0..0.01..10;

y = jn(z, 0);

Generates the values of *J*_{0}(*z*),
the Bessel function of the first kind for order 0 and inputs from 0 to
10.

## Remarks:

Bessel functions
are solutions to the differential equation:

where *ν* is the order, *J*_{ν}(*z*)
is a solution of the first kind and *Y*_{ν}(*z*) is a linearly independent solution
of the second kind For integer order *ν
= n:*

and

See BESSELJ
to evaluate the Bessel function of the first kind for non-integer orders.
Note that **z**
and **order** are reversed
for BESSELJ.

For integer orders, JN is faster than
BESSELJ.

See YN
to evaluate the Bessel function of the second kind for integer orders.

## See Also:

BESSELH

BESSELI

BESSELJ

BESSELK

BESSELY

YN