Differential Equations - Legendre Polynomials
Overview
The Legendre differential equation is
{% (1-x^2)\frac{dy^2}{dx^2} - 2x \frac{dy}{dx} + n(n+1)y = 0 %}
Legendre Polynomials
{% P_n(x) = \sum_{m=0}^M (-1)^m \frac{(2n-2m)!}{2^nm!(n-m)!(n-2m)!} x^{n-2m} %}