DLMF:6.7.E1

MaRDI QIDQ2952

• Label: DLMF:6.7.E1

Digital Library of Mathematical Functions ID 6.7.E1

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{t+b}\mathrm{d}t=\int_{0}^{\infty}\frac{e^{iat}}{t+ib}\mathrm{d}t=e^{ab}E_{1}\left(ab\right),}}$

Constraint(s)

${\displaystyle{\displaystyle b>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}$: exponential integral
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
 

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