Evaluates the Bessel function of the second kind for any real order.
BESSELY(v, z, opt)
v 
 
A real or real series, the order. The order must be real but need not be an integer.  
z 
 
Any scalar or series. The input value.  
opt 
 
Optional. An integer, the scaling method:

A scalar or series, the value of Y_{ν}(z) where ν is the order and z is the input.
bessely(0, 3)
returns 0.376850, the value of Y_{0}(3).
W1: 0..0.2..1;
W2: bessely(1, w1)
Returns Y_{1}(z) for z between 0 and 1. W2 contains the series
{inf, 3.323825, 1.780872, 1.260391, 0.978144, 0.781213}
bessely(3..9, 0..0.2..10)
Evaluates the Bessel function of the second kind for orders 3 through 9 with inputs from 0 to 10. Each column of the result contains the output for the specified order.
Bessel functions are solutions to the differential equation:
where ν is the order, Y_{ν}(z) is a solution of the second kind and J_{ν}(z) is a linearly independent solution of the first kind For noninteger order ν:
See YN for a faster evaluation of the Bessel function of the second kind for strictly integer orders.
If z is real and z < 0, the result is generally complex
See BESSELJ to evaluate J_{ν}(z), the Bessel function of the first kind.
BESSELY is based on a FORTRAN library written by D. E. Amos.
[1] Abramowitz and Stegun
Handbook of Mathematical Functions (9th printing 1970)
US Gov. Printing Office
Section 9.1.1, 9.1.89, 9.12
[2] Amos, D.E.
A Subroutine Package for Bessel Functions of a Complex
Argument and Nonnegative Order
Sandia National Laboratory Report
SAND851018, May, 1985.
[3] Amos, D.E.
A Portable Package for Bessel Functions of a Complex
Argument and Nonnegative Order
Trans. Math. Software, 1986