When to use Bessel functions of the first kind vs Neumann functions?

[ineedhlp]

When solving a differential equation for Bessel Functions, how do you know when to use the 1st kind or Neumann functions. How do you know which order of the bessel function to use?

 

[SteamKing]

It depends on the coefficients in the differential equation being solved.

e.g., Bessel's equation:

x^2*y'' + x*y' + (x^2 - α^2) = 0

Here, α is the order of the Bessel function which solves the equation.

http://en.wikipedia.org/wiki/Bessel_function

A Neumann function is a Bessel function of the second kind.

http://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html