DLMF:18.17.E40 (Q5781)

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Language	Label	Description	Also known as
English	DLMF:18.17.E40	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-ax}L^{(\alpha)}_{n}\left(bx% \right)x^{z-1}\mathrm{d}x=\frac{\Gamma\left(z+n\right)}{n!}\*{(a-b)^{n}}a^{-n-% z}\*{{}_{2}F_{1}}\left({-n,1+\alpha-z\atop 1-n-z};\frac{a}{a-b}\right),}}

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DLMF:18.17.E40

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

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

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Defining formula

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

C5.S2.E1.m2apdec

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Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5adec

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Defining formula

{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r12.m2aidec

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Defining formula

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

C1.S4.SS4.m1aamdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2asdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5amdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aamdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1gdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1amdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1akdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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