Formula:3414

Digital Library of Mathematical Functions ID 8.20.E3

${\displaystyle{\displaystyle E_{p}\left(z\right)\sim\pm\frac{2\pi i}{\Gamma\left(p\right)}e^{\mp p\pi i}z^{p-1}+\frac{e^{-z}}{z}\sum_{k=0}^{\infty}\frac{(-1)^{k}{\left(p\right)_{k}}}{z^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z\leq\tfrac{7}{2}\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$: generalized exponential integral
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle p}}$: parameter
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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