Formula:6701

Digital Library of Mathematical Functions ID 18.30.E7

${\displaystyle{\displaystyle P_{n}\left(x;c\right)=\sum_{\ell=0}^{n}\frac{c}{\ell+c}P_{\ell}\left(x\right)P_{n-\ell}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x};\NVar{c}\right)}}$: associated Legendre polynomial
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle n}}$: continuous nonnegative real
 

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