DLMF:14.17.E5 (Q4886): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:14.17.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{1}x^{\sigma}\left(1-x^{2}\right)^{\mu/2}% \mathsf{P}^{-\mu}_{\nu}\left(x\right)\mathrm{d}x=\frac{\Gamma\left(\frac{1}{2}% \sigma+\frac{1}{2}\right)\Gamma\left(\frac{1}{2}\sigma+1\right)}{2^{\mu+1}% \Gamma\left(\frac{1}{2}\sigma-\frac{1}{2}\nu+\frac{1}{2}\mu+1\right)\Gamma% \left(\frac{1}{2}\sigma+\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{2}\right)},}}

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DLMF:14.17.E5

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{\displaystyle{\displaystyle\Re\sigma>-1}}

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{\displaystyle{\displaystyle\Re\mu>-1}}

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Defining formula

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

C5.S2.E1.m2adec

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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{d}\NVar{x}}}

C1.S4.SS4.m1addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1ddec

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Sitelinks

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