# Rodrigues' Formula for Legendre Polynomials

## Theorem

$\map {P_n} x = \dfrac 1 {2^n n!} \dfrac {\d^n} {\d x^n} \paren {x^2 - 1}^n$

where $P_n$ is the $n$th Legendre polynomial.

## Source of Name

This entry was named for Olinde Rodrigues.