DLMF:14.3.E18 (Q4707)

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Language	Label	Description	Also known as
English	DLMF:14.3.E18	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=2^{-\mu}x^{\nu-\mu}% \left(x^{2}-1\right)^{\mu/2}\mathbf{F}\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu,% \tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2};\mu+1;1-\frac{1}{x^{2}}\right),}}

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DLMF:14.3.E18

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Defining formula

{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C14.S21.SS1.p1.m1afdec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2andec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1qdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1mdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1pdec

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