According to __ http://mathworld.wolfram.com/ExponentialIntegral.html__, the exponential integral is defined in the following manner:

/ ∞ / | -t ei(x) = - \ e = -E (-x) \ ----- dt 1 | t / / -x

where E_{1} 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The notation ei(x) is (thus far) merely retained from its historical context; it has otherwise been superceded by the En-function (see __ http://mathworld.wolfram.com/En-Function.html__ for more info).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.*