Consider the exponential integral of the complex argument defined by $$ Ei( z ) = \gamma + \ln(-z) +\sum\limits_{ n = 1 }^{ \infty } \frac{ z^n }{n n!}, $$ where $ z \in \mathbb{C} \backslash ( \mathbb{R}_+ \cup 0 ) $, $ \gamma $ is the Euler-Mascheroni constant.
It is rather easy to show that $ | Ei( z ) | \leq C \frac{ e^{ \Re z } }{ | z | } $. Do you know any reference for this result? Some handbook of integrals or of special functions, maybe? (This estimate is not difficult to prove, but I don't think this fact deserves to have a separate proof in the paper. I think it must have be stated somewhere in literature.) Thanks in advance!