I recently ran across a problem where I can reduce an integral to the form $\int_{0}^{(1+i)R} e^{-ax^2} \,dx$, I want to find the solution as $R$ goes to infinity. Since the integral looks to be a Gaussian integral, is the solution $\frac{\sqrt{\pi}}{2\sqrt{a}}$? Or is this incorrect since the Gaussian Integral is only for the real line?
2026-04-01 13:12:10.1775049130
Gaussian integral over complex interval
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