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Never mind, thanks to the comment by J. M. I found the source of this expression. The series are connected to the exponential integral: $$\text{Ei}(t)=-\int_{-t}^{\infty} \frac{e^{-p}}{p} dp=\gamma+\log |t|+\sum_{n=1}^{\infty} \frac{t^n}{n!n}$$ The continued fraction turns out to be a particular case of incomplete Gamma function: $$\Gamma ...



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