DLMF:18.17.E10 (Q5751)

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Language	Label	Description	Also known as
English	DLMF:18.17.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{x^{\beta+\mu}(x+1)^{n}}{\Gamma\left(\beta+% \mu+n+1\right)}P^{(\alpha,\beta+\mu)}_{n}\left(\frac{x-1}{x+1}\right)=\int_{0}% ^{x}\frac{y^{\beta}(y+1)^{n}}{\Gamma\left(\beta+n+1\right)}P^{(\alpha,\beta)}_% {n}\left(\frac{y-1}{y+1}\right)\*\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}% \mathrm{d}y,}}

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DLMF:18.17.E10

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{\displaystyle{\displaystyle x>0}}

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Defining formula

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

C5.S2.E1.m2abdec

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Defining formula

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

C18.S3.T1.t1.r2.m2abdec

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Defining formula

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

C1.S4.SS4.m1aidec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aidec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1edec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1idec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1gdec

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