DLMF:18.18.E15 (Q5805)

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Language	Label	Description	Also known as
English	DLMF:18.18.E15	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(\frac{1+x}{2}\right)^{n}=\frac{{\left(\beta+% 1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\frac{\alpha% +\beta+2\ell+1}{\alpha+\beta+1}\frac{{\left(\alpha+\beta+1\right)_{\ell}}{% \left(n-\ell+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+% \beta+2\right)_{\ell}}}P^{(\alpha,\beta)}_{\ell}\left(x\right),}}

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DLMF:18.18.E15

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Defining formula

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

C18.S3.T1.t1.r2.m2addec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1acdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1ndec

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