DLMF:18.17.E9 (Q5750)

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Language	Label	Description	Also known as
English	DLMF:18.17.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{(1-x)^{\alpha+\mu}P^{(\alpha+\mu,\beta-\mu)}% _{n}\left(x\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{x}^{1}\frac{(1-y)% ^{\alpha}P^{(\alpha,\beta)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}% \frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y,}}

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DLMF:18.17.E9

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{\displaystyle{\displaystyle-1<x<1}}

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1ahdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ahdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1hdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1fdec

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Sitelinks

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