I want to solve this integral $$ \int_{0}^{\infty}\int_{0}^{2\pi}\exp(-ar^2)\exp(r\,b(\cos\theta+\sin\theta))r^{m}\cos^{m}(2\theta)d\theta \,dr,$$ where $a$ and $b$ are constants. I know how to solve this integral when $b=0$. I need some suggestions from experts to solve this integral. Of course, I can expand the second exponential function containing sine and cosine as a power series then I can write the integral as a complicated summation over many indices containing gamma functions and beta functions. I need a very simple result, If somebody can connect this to another special functions, I will be happy.
2026-04-13 12:02:22.1776081742
Integral Involving Trigonometric Functions and Exponential (Related to Marcum Q-function)
293 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DEFINITE-INTEGRALS
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