Dear everyone,

Hi,

How to derive that equation (5.1.11 in Abramowitz and Stegun)

$E_1(z)= - \gamma - \mathrm{ln} z - \sum_{n=1}^{\infty}\frac{ (-1)^n z^n}{n n!} (|arg z|< \pi)$

Thank you very much in advance!!

here the $E_1(z)$ is defined as $E_1(z):=\int_z^{\infty} \frac{ e^{-t} }{t}$.