DLMF:18.17.E16 (Q5757): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.17.E16	No description defined

Statements

Defining formula

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

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DLMF:18.17.E16

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Defining formula

{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

C5.S12.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.m2addec

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Defining formula

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

C16.S2.m7adec

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Defining formula

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

C1.S4.SS4.m1aodec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2acdec

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