/inf
Ei(x) = |    exp(-t)/t dt
        /x

for x > 0.

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The notation ei(x) is (thus far) merely retained from its historical context; it has otherwise been superceded by the En-function (see http://mathworld.wolfram.com/En-Function.html for more info).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