DLMF:18.17.E41 (Q5782)

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Language	Label	Description	Also known as
English	DLMF:18.17.E41	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}\mathit{He}_{n}\left(x% \right)x^{z-1}\mathrm{d}x=\Gamma\left(z+n\right)a^{-n-2}{{}_{2}F_{2}}\left({-% \tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}\atop-\tfrac{1}{2}z-\tfrac{1}{2}n,-% \tfrac{1}{2}z-\tfrac{1}{2}n+\tfrac{1}{2}};-\tfrac{1}{2}a^{2}\right),}}

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DLMF:18.17.E41

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{\displaystyle{\displaystyle\Re a>0}}

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{\displaystyle{\displaystyle\Re z>0}}

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{\displaystyle{\displaystyle\Re z>-1}}

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{\displaystyle{\displaystyle\Re z>0}}

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{\displaystyle{\displaystyle n}}

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{\displaystyle{\displaystyle\Re z>-1}}

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Defining formula

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

C5.S2.E1.m2aqdec

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Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}

C16.S2.m1adec

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Defining formula

{\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}

C18.S3.T1.t1.r14.m2ahdec

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Defining formula

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

C1.S4.SS4.m1aandec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2atdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aandec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1afdec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1hdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1andec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1aldec

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Sitelinks

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