Euler polynomials, Bernoulli polynomials, and Lévy's stochastic area formula

Nobuyuki Ikeda, Setsuo Taniguchi

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Abstract

In 1951, P. Lévy represented the Euler and Bernoulli numbers in terms of the moments of Lévy's stochastic area. Recently the authors extended his result to the case of Eulerian polynomials of types A and B. In this paper, we continue to apply the same method to the Euler and Bernoulli polynomials, and will express these polynomials with the use of Lévy's stochastic area. Moreover, a natural problem, arising from such representations, to calculate the expectations of polynomials of the stochastic area and the norm of the Brownian motion will be solved.

Original languageEnglish
Pages (from-to)684-694
Number of pages11
JournalBulletin des Sciences Mathematiques
Volume135
Issue number6-7
DOIs
Publication statusPublished - Sep 1 2011

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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