Euler's formulae for ζ(2n) and products of Cauchy variables

Paul Bourgade, Takahiko Fujita, Marc Yor

Research output: Contribution to journalArticle

Abstract

We show how to recover Euler's formula for ζ(2n), as well as L χ4(2n + 1), for any integer n, from the knowledge of the density of the product ℂ1, ℂ2 . . . , ℂk, for any k ≥ 1, where the ℂi's are independent standard Cauchy variables.

Original languageEnglish (US)
Pages (from-to)81-88
Number of pages8
JournalElectronic Communications in Probability
Volume12
StatePublished - Apr 7 2007

Keywords

  • Cauchy variables
  • Euler numbers
  • Planar Brownian motion
  • Stable variables

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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