Article contents
Probabilistic Proofs of Euler Identities
Published online by Cambridge University Press: 30 January 2018
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © Applied Probability Trust
References
- 2
- Cited by