DLMF:8.19.E24

MaRDI QIDQ3408

• Label: DLMF:8.19.E24

Digital Library of Mathematical Functions ID 8.19.E24

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}E_{n}\left(t\right)\mathrm{d}t=\frac{(-1)^{n-1}}{a^{n}}\left(\ln\left(1+a\right)+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>-1}}$
${\displaystyle{\displaystyle n=1,2,\dots}}$
${\displaystyle{\displaystyle\Re a>-1}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$: generalized exponential integral
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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