DLMF:18.17.E1 (Q5742)

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Language	Label	Description	Also known as
English	DLMF:18.17.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle 2n\int_{0}^{x}(1-y)^{\alpha}(1+y)^{\beta}P^{(% \alpha,\beta)}_{n}\left(y\right)\mathrm{d}y=P^{(\alpha+1,\beta+1)}_{n-1}\left(% 0\right)-(1-x)^{\alpha+1}(1+x)^{\beta+1}P^{(\alpha+1,\beta+1)}_{n-1}\left(x% \right).}}

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DLMF:18.17.E1

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Defining formula

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

C18.S3.T1.t1.r2.m2adec

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Defining formula

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

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1dec

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