Formula:5460

Digital Library of Mathematical Functions ID 14.7.E11

${\displaystyle{\displaystyle P^{m}_{n}\left(x\right)=\left(x^{2}-1\right)^{m/2}\frac{{\mathrm{d}}^{m}}{{\mathrm{d}x}^{m}}P_{n}\left(x\right),}}$

Symbols List

• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$: Legendre polynomial
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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