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 Lχ4 (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)73-80
Number of pages8
JournalElectronic Communications in Probability
Volume12
DOIs
StatePublished - Jan 1 2007

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Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Euler’s formulae for ζ(2n) and products of cauchy variables. / Bourgade, Paul; Fujita, Takahiko; Yor, Marc.

In: Electronic Communications in Probability, Vol. 12, 01.01.2007, p. 73-80.

Research output: Contribution to journalArticle

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