Generalized Incomplete Gamma Function and Exponential

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On the site mathwolfram si possible to see the properties of the exponetial function at

http://functions.wolfram.com/GammaBetaErf/ExpIntegralEi/introductions/ExpIntegrals/ShowAll.html

It is related to the incomplete generalized $\Gamma(a,z_1,z_2)$. I have a particular case for the Gamma function

indeed is $\Gamma(-s,0, z=\pm i)$ which is related to the The exponetial function in the formula given by mathwolfram site

$\Gamma(-s,0,z) = - (z_2)^{-s} E_{-s-1}(z)$ the definition of E on mathwolfram site say that $Re(z)>0$ but I have a limit case with $(\pm i)$.

I would like to know if the definition is valid ( sometimes there could be a print error it not the first time I see) in the limit case for every z.

Further the site say a property that $E_s(x+i \epsilon) \rightarrow E_s(x)$ but still for limit case $Re\{x\}<0$

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I found a definition in the online digital library and I could check that E is defined for all $z \in C$. The math wolfram report a documentation imperfect. I could also found another error in mathwolfram documentation but the calculator report the exact result.