- #26

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The sum should have been$$I(\theta)=\int_0^{2\pi} \sum_{m=0}^{\infty}\frac{cos(m\theta)}{m!}d\theta$$I was to hasty with typing latex. I think that sum converges.Unfortunately, the sum under your integral sign doesn't converge (for any ##\theta##). I think you lost your factorial term.