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Four derivations of an interesting bilateral series generalizing the series for zeta of 2. (English)
Int. J. Math. Educ. Sci. Technol. 44, No. 3, 456-461 (2013).
Summary: We present four derivations of the closed form of the partial fractions expansion $$π\left(\dfrac{\cot πa}{b-a}-\dfrac{\cot πb}{a-b}\right) = \sum_{n=-\infty}^{\infty}\dfrac{1}{(n+a)(n+b)}.$$ This interesting series is a generalization of the series $\frac{π^2}{6}= \sum_{n=1}^{\infty} \frac{1}{n^2} = ζ(2)$ made famous by Euler.
Classification: F65 I45 I55
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