### 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 ℂ_{1}, ℂ_{2} . . . , ℂ_{k}, for any k ≥ 1, where the ℂ_{i}'s are independent standard Cauchy variables.

Original language | English (US) |
---|---|

Pages (from-to) | 81-88 |

Number of pages | 8 |

Journal | Electronic Communications in Probability |

Volume | 12 |

State | Published - Apr 7 2007 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Electronic Communications in Probability*,

*12*, 81-88.

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

Research output: Contribution to journal › Article

*Electronic Communications in Probability*, vol. 12, pp. 81-88.

}

TY - JOUR

T1 - Euler's formulae for ζ(2n) and products of Cauchy variables

AU - Bourgade, Paul

AU - Fujita, Takahiko

AU - Yor, Marc

PY - 2007/4/7

Y1 - 2007/4/7

N2 - 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.

AB - 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.

KW - Cauchy variables

KW - Euler numbers

KW - Planar Brownian motion

KW - Stable variables

UR - http://www.scopus.com/inward/record.url?scp=34147169571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34147169571&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 81

EP - 88

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

ER -