# Proof of the Rodrigues formula for the Legendre polynomials

1. Jan 11, 2016

### Happiness

How is the below expression for $a_{n-2k}$ motivated?

I verified that the expression for $a_{n-2k}$ satisfies the recurrence relation by using $j=n-2k$ and $j+2=n-2(k-1)$ (and hence a similar expression for $a_{n-2(k-1)}$), but I don't understand how it is being motivated.

Source: http://www.phys.ufl.edu/~fry/6346/legendre.pdf

2. Jan 16, 2016