DLMF:8.19.E8

MaRDI QIDQ3392

• Label: DLMF:8.19.E8

Digital Library of Mathematical Functions ID 8.19.E8

${\displaystyle{\displaystyle E_{n}\left(z\right)=\frac{(-z)^{n-1}}{(n-1)!}(\psi\left(n\right)-\ln z)-\sum_{\begin{subarray}{c}k=0\\ k\neq n-1\end{subarray}}^{\infty}\frac{(-z)^{k}}{k!(1-n+k)},}}$

Symbols List

• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$: generalized exponential integral
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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