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 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:

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:

$image\jn01.gif$

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.

JN

Purpose:

Syntax:

Returns:

Example:

Example:

Remarks:

See Also: