DLMF:18.17.E33 (Q5774)

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Language	Label	Description	Also known as
English	DLMF:18.17.E33	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{-1}^{1}e^{-(x+1)z}P^{(\alpha,\beta)}_{n}% \left(x\right)(1-x)^{\alpha}(1+x)^{\beta}\mathrm{d}x=\frac{(-1)^{n}2^{\alpha+% \beta+n+1}\Gamma\left(\alpha+n+1\right)\Gamma\left(\beta+n+1\right)}{\Gamma% \left(\alpha+\beta+2n+2\right)n!}z^{n}{{}_{1}F_{1}}\left({\beta+n+1\atop\alpha% +\beta+2n+2};-2z\right),}}

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DLMF:18.17.E33

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{\displaystyle{\displaystyle z\in\mathbb{C}}}

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Defining formula

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

C5.S2.E1.m2aldec

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Defining formula

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

C18.S3.T1.t1.r2.m2aedec

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Defining formula

{\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}% \right)}}

C16.S2.m7aadec

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Defining formula

{\displaystyle{\displaystyle\mathbb{C}}}

introduction.Sx4.p1.t1.r1.m2adec

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Defining formula

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

C1.S4.SS4.m1aafdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2adec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2apdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5aidec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aafdec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1dec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1afdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1addec

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Sitelinks

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