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:

 

image\bessy01.gif

 

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:

 

image\yn01.gif

 

and

 

image\yn02.gif

 

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