Besssel and legendre's equation

[Wishbone]

Hi, I need a little clarification about these two functions.

One question I have is what is the irregular solution of the bessel function? I know it has a irregular singularities, but I am asked to talk about the irregular solution of the bessel function, and I'm not sure what to say about it, or what it is.


Secondly, the question reads what happens if we choose s=-1 from the indicial equation for the legendre's equation. The problem is I don't know of any s in the indicial equation. Could s be the same as n?

(n+1)(n+2)a_(n+2)+[-n(n+1)+l(l+1)]a_n==0

 

[Galileo]

I know that for integer n, the solution $Y_n(x)$ (n-th Bessel function of the second kind) has a singularity at x=0. So I guess that's the irregular solution. The first kind solutions $J_n(x)$ are defined everywhere.