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 Jn(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 J1(3).

Example:

z = 0..0.01..10;

y = jn(z, 0);

 

Generates the values of J0(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:

 

image\bessy01.gif

 

where ν is the order, Jν(z) is a solution of the first kind and Yν(z) is a linearly independent solution of the second kind For integer order ν = n:

 

image\jn01.gif

 

and

 

image\jn02.gif

 

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