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]> legendre_3

\begin{array}{rcl} P_{l}^{- m} (x) & = & {(- 1)}^{m} \frac{(l - m)!}{(l + m)!} P_{l}^{m} (x) \\ P_{- l - 1}^{m} (x) & = & P_{l}^{m} (x) \end{array}