Two different functions of real argument x \in \mathbb{R} are called this way:
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which are related to each other as:
(3) | {\rm Ei}(x) = - E_1(-x) |
There is a trend to moving from \rm Ei definition which was dominating in the past towards \rm E_1.
For the small arguments |x| \ll 1 it can be expressed as slowly converging sum:
(4) | {\rm Ei}(x) = \gamma + \ln |x| + \sum_{k=1}^{\infty} \frac{x^k}{k \cdot k!}, \quad x>0 |
where \gamma = 0.577 ... is Euler–Mascheroni constant.