I want to solve this equation
∂2ρϕ+3ρ∂ρϕ+(M2(1+ρ2)2−l(l+2)ρ2)ϕ=0
numerically.
I know that this equation can be transformed into the hypergeometric equation through the transformation
ϕ(ρ)=ρl(1+ρ2)−αP(ρ)
(in which
P is some function)
whose exact solution is the well known function
see here
2F1(a,b;c;ρ)=∞∑n=0(a)n(b)n(c)nρnn!.
The crucial characteristic of this function is that if a or b are negative integers, then the series is finite.
However, I'm interested in exploring a numerical solution for this equation and I would like to know how to obtain numerically the finite series solutions.
Any idea?
Thanks.
This post imported from StackExchange Mathematics at 2015-05-09 14:49 (UTC), posted by SE-user miguelFe