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## Main Question or Discussion Point

How do I calculate the integral

[tex]\int_{ix}^{i\infty} e^{-t} t^{-s-1}dt,[/tex]

where [itex]x>0[/itex], [itex]s>0[/itex]? Mathematica gives [itex]\Gamma(-s,ix)[/itex], where [itex]\Gamma(\cdot,\cdot)[/itex] is the incomplete gamma function, but I am not sure how to justify this formally.

[tex]\int_{ix}^{i\infty} e^{-t} t^{-s-1}dt,[/tex]

where [itex]x>0[/itex], [itex]s>0[/itex]? Mathematica gives [itex]\Gamma(-s,ix)[/itex], where [itex]\Gamma(\cdot,\cdot)[/itex] is the incomplete gamma function, but I am not sure how to justify this formally.