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This is gamma function: $\Gamma (n) = \int_0^\infty x^{n-1}e^{-x}\,dx$ What will be Result if I add Imaginary Number to Exponential of Euler Gamma Function?

$$? = \int_0^\infty x^{n-1}e^{-ix}\,dx$$

where the $i^2=-1$

isn't it a new function!? it will and will not converge?

3 Answers 3