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Probabilistic proofs of euler identities
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 50, no 4, 1206-1212 p.Article in journal (Refereed) Published
Abstract [en]

Formulae for zeta(2n) and L-chi 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 zeta(2) = pi(2)/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.

Place, publisher, year, edition, pages
2013. Vol. 50, no 4, 1206-1212 p.
Keyword [en]
Basel problem, hyperbolic secant distribution, Euler number, tangent number, Euler's sine product
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-142523DOI: 10.1239/jap/1389370108ISI: 000330929400020Scopus ID: 2-s2.0-84892739679OAI: oai:DiVA.org:kth-142523DiVA: diva2:703344
Note

QC 20140306

Available from: 2014-03-06 Created: 2014-03-06 Last updated: 2017-12-05Bibliographically approved

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