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[tex]\int_{0}^{1} t^{x-1} e^{-t} dt =\sum_{n=0}^{\infty} \frac{(-1)^n}{(x+n)n!}[/tex]

And I don't see how to arrive at this identity, I guess he expands t in the integrand but my memory is rusty as to this series expansion.

Thanks in advance.