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@wikipedia
Two different functions are called this way:
(1) |
{\rm Ei}(x) = - \int_{-x}^{\infty} \frac{e^{-\xi}}{\xi} \, d\xi |
|
(2) |
{\rm E_1}(x) = \int_{x}^{\infty} \frac{e^{-\xi}}{\xi} \, d\xi |
|
which are related to each other as:
(3) |
{\rm Ei}(x) = - E_1(-x) |
For the positive argument
x>0 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 |