I am trying to solve the following integral $\int_{0}^{2\pi}{\left|\int_{0}^{2\pi}{e^{ik\cos\left(\theta-\varphi\right)}\cos\left(n\theta\right)}d\theta\right|^2 d\varphi},\ \ n=0,1,2,.......$ which gives the eigenvalues of some integral operator. Obviously the calculation will be done numerically with MATLAB but my problem is the absolute value which is outside of the integral. Can anyone help?
2026-05-11 08:19:24.1778487564
Integral calculation for eigenvalues
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