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The double-angle formula, $\sin2x=2\sin x\cos x$, turns the scary-looking integral $$\int_0^{\infty}dz\prod_{k=1}^{\infty}\cos\frac{z}{2^k}$$ into fun once you realize $\prod_k\cos\frac{z}{2^k}=\frac{\...

I'm using the Euler–Maclaurin formula in a research project I'm working on. While brilliant, the elementary proof found in Apostol - An Elementary View of Euler's Summation Formula does not give me ...