YN

Purpose:

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

YN(z, order)

z	-	A series or scalar.
order	-	Optional. An integer, the order. Defaults to 0.

A real, series, or table the value of Y_n(z) where z is the input and n is the integer order.

yn(3.0,1)

returns 0.3246, the value of Y₁(3).

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.

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:

$image\yn01.gif$

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.