DLMF:8.19.E25 (Q2711)

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Language	Label	Description	Also known as
English	DLMF:8.19.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}t^{b-1}E_{p}\left(t\right)% \mathrm{d}t=\frac{\Gamma\left(b\right)(1+a)^{-b}}{p+b-1}\*F\left(1,b;p+b;a/(1+% a)\right),}}

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DLMF:8.19.E25

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

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{\displaystyle{\displaystyle\Re(p+b)>1}}

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Defining formula

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

C5.S2.E1.m2aedec

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$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

C15.S2.E1.m2adec

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Defining formula

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

C1.S4.SS4.m1afdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aodec

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generalized exponential integral

Defining formula

{\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}

C8.S19.E1.m2aacdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

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Defining formula

{\displaystyle{\displaystyle a}}

C8.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle p}}

C8.S1.XMD4.m1pdec

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Sitelinks

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