I am trying to come up with a generic formula for the below integral, which is analogous to the upper incomplete gamma function, Clear[x, t, n]; x1 = FullSimplify[Integrate[(1 + I t)^(-1 - I x) E^(2 \[Pi] I n t) , {t, 0, 1}, Assumptions -> x > 0 && n > 0]] I used assumptions to increase the likelihood of getting a correct answer. It gives me the not so neat function below: But I usually don't blindly trust Mathematica's results, so I tried to validate the formula it gave me, Clear[t]; x = 2; ...
