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@wikipedia


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{\rm Ei}(x) = - \int_{-x}^{\infty} \frac{e^{-\xi}}{\xi} \, d\xi


for For the positive argument 

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it can be decomposed into expressed as slowly converging sum:

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{\rm Ei}(x) = \gamma + \ln x + \sum_{k=1}^{\infty} \frac{x^k}{k \cdot k!}, \quad x>0

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