Formula:3388

Digital Library of Mathematical Functions ID 8.19.E4

${\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{z^{p-1}e^{-z}}{\Gamma\left(p\right)}\int_{0}^{\infty}\frac{t^{p-1}e^{-zt}}{1+t}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}$
${\displaystyle{\displaystyle\Re p>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: 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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle p}}$: parameter
 

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