2 Infinite Series Solved using Complex Analysis
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2 Infinite Series Solved using Complex Analysis
Here we evaluate a couple of trigonometric series $C=sum_{k=0}^{infty}cos(kx)/(2k+1)$ and $S=sum_{k=0}^{infty}sin(kx)/(2k+1)$ using some beautiful complex analysis via Euler's formula and laurent series expansions leading to closed forms that are definitely real numbers WOW do they look complex, if you know what I mean. Techniques covered ...
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