# YN

## Purpose:

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

## Syntax:

YN(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 Yn(z) where z is the input and n is the integer order.

## Example:

yn(3.0,1)

returns 0.3246, the value of Y1(3).

## Example:

z = 0..0.01..1;

y = yn(z, 1);

Returns Y1(z), the values of the Bessel function of the second kind for order 1 and inputs from 0 to 1.

## Remarks:

Bessel functions are solutions to the differential equation:

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

and

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

For integer orders, YN is faster than BESSELY.

See JN to evaluate the Bessel function of the first kind for integer orders.