DLMF:14.15.E24 (Q4871)

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Language	Label	Description	Also known as
English	DLMF:14.15.E24	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{1}{% \left(\nu+\frac{1}{2}\right)^{1/4}2^{(\nu+\mu)/2}\Gamma\left(\frac{1}{2}\nu+% \frac{1}{2}\mu+\frac{3}{4}\right)}\left(\frac{\zeta^{2}-\alpha^{2}}{x^{2}-a^{2% }}\right)^{1/4}\*\left(U\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}% \zeta\right)+O\left(\nu^{-2/3}\right)\mathrm{env}\mskip-1.0mu U\left(\mu-\nu-% \tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)\right),}}

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DLMF:14.15.E24

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2andec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2afdec

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Ferrers function of the first kind

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}% \right)}}

C14.S15.SS5.p1.m7aadec

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Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1odec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1qdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1qdec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1dec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C14.S15.XMD14.m1dec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD9.m1gdec

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Sitelinks

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