Bonnet's Recursion Formula

Theorem

Let $\map {P_n} x$ denote the Legendre polynomial of order $n$.

Bonnet's Recursion Formula states:

$\paren {n + 1} \map {P_{n + 1} } x = \paren {2 n + 1} x \map {P_n} x - n \map {P_{n - 1} } x$

Proof

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Source of Name

This entry was named for Pierre Ossian Bonnet.