Abstract
Formulae for ζ(2n) and Lχ4(2n + 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel problem, where ζ(2) = π2 / 6, is considered. Euler's infinite product for the sine is also proved using the distribution of sums of independent hyperbolic secant random variables and a local limit theorem.
Citation
Lars Holst. "Probabilistic proofs of Euler identities." J. Appl. Probab. 50 (4) 1206 - 1212, December 2013. https://doi.org/10.1239/jap/1389370108
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