Probabilistic proofs of euler identities

• Autores: Lars Holst
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 4, 2013, págs. 1206-1212
• Idioma: inglés
• DOI: 10.1017/s0021900200013887
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• Resumen

  • Formulae for £(2n) and L?4 (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 ?(2) = p²/6, 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