According to http://mathworld.wolfram.com/ExponentialIntegral.html, the exponential integral is defined in the following manner:
ei(x) = - \ e = -E (-x)
\ ----- dt 1
where E1 is the En-function with n=1. Note that ei(ln(x))=Li(x) where Li(x) is defined in the same way as it is in the prime number theorem.
The notation ei(x) is (thus far) merely retained from its historical context; it has otherwise been superceded by the En-function (see http://mathworld.wolfram.com/En-Function.html for more info).
All information "stolen" from mathworld. Just trying to get the facts right.