DLMF:18.18.E1 (Q5791)

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Language	Label	Description	Also known as
English	DLMF:18.18.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle a_{n}=\frac{n!(2n+\alpha+\beta+1)\Gamma\left(n+% \alpha+\beta+1\right)}{2^{\alpha+\beta+1}\Gamma\left(n+\alpha+1\right)\Gamma% \left(n+\beta+1\right)}\*\int_{-1}^{1}f(x)P^{(\alpha,\beta)}_{n}\left(x\right)% (1-x)^{\alpha}(1+x)^{\beta}\mathrm{d}x.}}

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DLMF:18.18.E1

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Symbols defined

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Defining formula

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

C5.S2.E1.m2adec

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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!}}

introduction.Sx4.p1.t1.r15.m5adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1dec

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Defining formula

{\displaystyle{\displaystyle f(z)}}

C18.S18.XMD1.m1dec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1dec

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