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Machinato

2,86319 silver badges33 bronze badges

earned this badge 4 times.

Closed form for $\sum_{n=-\infty}^{\infty}\frac{1}{(n-a)^2+b^2}$.

Awarded Jul 18 at 13:50

The Basel problem

Awarded Nov 10, 2021 at 22:40

Proof of $\sum_{n=1}^{\infty}\frac1{n^3}\frac{\sinh\pi n\sqrt2-\sin\pi n\sqrt2}{{\cosh\pi n\sqrt2}-\cos\pi n\sqrt2}=\frac{\pi^3}{18\sqrt2}$

Awarded Dec 12, 2019 at 22:20

Evaluating the series $\sum_{n=1}^{\infty} \frac{n}{e^{2 \pi n}-1}$ using the inverse Mellin transform

Awarded Jul 24, 2016 at 14:19

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