# Limit change of variable legality?

by Pengwuino
Tags: legality, limit, variable
 PF Gold P: 7,120 1. The problem statement, all variables and given/known data $$\mathop {\lim }\limits_{x - > 1} \ln (1 - x)(P_{l - 1} (x) - xP_l (x)) - \mathop {\lim }\limits_{x - > - 1} \ln (1 + x)(P_{l - 1} (x) - xP_l (x))$$ where $$P_{l}$$ are the Legendre Polynomials. 2. Relevant equations Legendre polynomial recursion relations I suppose 3. The attempt at a solution So in trying to determine this limit. L'Hospitals rule doesn't come up with anything useful seemingly. However, would it be mathematically legal to switch the limit of the right side to x-> 1 and switch out every x for -x? I can't seem to figure out this limit. If this were legal, I think I could determine this limit for l = 0 using this idea but for an arbitrary l I don't think this would work. Anyone got any tips? :)