Euler’s formulae for ζ(2n) and products of cauchy variables

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. © 2007 Applied Probability Trust.