Euler's formulae for ζ(2n) and products of Cauchy variables
Paul Bourgade, Laboratoire de probabilités et modèles aléatoires, université Paris 6
Takahiko Fujita, Graduate School of Commerce and management, Hitotsubashi University
Marc Yor, Laboratoire de probabilités et modèles aléatoires, université Paris 6
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
of independent standard Cauchy variables.
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