# 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
Y_{n}(z)
where z is the input and n is
the integer order.

## Example:

yn(3.0,1)

returns 0.3246, the value of Y_{1}(3).

## Example:

z = 0..0.01..1;

y = yn(z, 1);

Returns Y_{1}(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 *J*_{ν}(*z*)
is a solution of the first kind. *Y*_{ν}(*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.

## See Also:

BESSELH

BESSELI

BESSELJ

BESSELK

BESSELY

JN