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

Nobuyuki Ikeda, Setsuo Taniguchi

研究成果: ジャーナルへの寄稿学術誌査読

1 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)684-694
ページ数11
ジャーナルBulletin des Sciences Mathematiques
135
6-7
DOI
出版ステータス出版済み - 9月 2011

!!!All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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