- #1

member 428835

## Homework Statement

Simplify $$\int_{-1}^1\left( (1-x^2)P_i''-2xP'_i+2P_i\right)P_j\,dx$$

where ##P_i## is the ##i^{th}## Legendre Polynomial, a function of ##x##.

## Homework Equations

## The Attempt at a Solution

Integration by parts is likely useful?? Also I know the Legendre Polynomials are orthogonal on ##[-1,1]##. Before simply trying integration by parts term-wise I was trying to see if the equi-dimensional equation ##(1-x^2)P_i''-2xP'_i+2P_i## could first be expressed in a more simple manner? Any thoughts?