Formula:5544

Digital Library of Mathematical Functions ID 14.15.E1

${\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(\pm x\right)=\left(\frac{1\mp x}{1\pm x}\right)^{\mu/2}\left(\sum_{j=0}^{J-1}\frac{{\left(\nu+1\right)_{j}}{\left(-\nu\right)_{j}}}{j!\Gamma\left(j+1+\mu\right)}\left(\frac{1\mp x}{2}\right)^{j}+O\left(\frac{1}{\Gamma\left(J+1+\mu\right)}\right)\right)}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle J}}$: nonnegative integer
 

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