Rodrigues' Formula for Legendre Polynomials

Theorem

 * $\displaystyle P_n\left({x}\right) = \frac 1 {2^n n!} \frac {\mathrm d^n} {\mathrm d x^n} \left({x^2 - 1}\right)^n$

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