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.

Proof

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Source of Name

This entry was named for Olinde Rodrigues.

Sources

• 1920: E.T. Whittaker and G.N. Watson: A Course of Modern Analysis (3rd ed.): $15.11$: Rodrigues' formula for the Legendre polynomials.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Rodrigues's formula