DLMF:18.18.E14 (Q5804)

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Language	Label	Description	Also known as
English	DLMF:18.18.E14	No description defined

Statements

Defining formula

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

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DLMF:18.18.E14

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Defining formula

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

C18.S3.T1.t1.r2.m2acdec

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Defining formula

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

C5.S2.SS3.m1abdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5agdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1mdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1jdec

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