Vol. 3, No. 3, 2010

Download this article
Download this article For screen
For printing
Recent Issues
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 5
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
Cover Page
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
$\zeta(n)$ via hyperbolic functions

Joseph D’Avanzo and Nikolai A. Krylov

Vol. 3 (2010), No. 3, 289–296
Abstract

We present an approach to compute ζ(2) by changing variables in the double integral using hyperbolic trigonometric functions. We also apply this approach to present ζ(n), when n > 2, as a definite improper integral of a single variable.

Keywords
multiple integrals, Riemann's zeta function
Mathematical Subject Classification 2000
Primary: 26B15
Secondary: 11M06
Milestones
Received: 13 November 2009
Accepted: 29 June 2010
Published: 16 October 2010

Communicated by Ken Ono
Authors
Joseph D’Avanzo
Siena College
Department of Mathematics
515 Loudon Road
Loudonville, NY 12211
United States
Nikolai A. Krylov
Siena College
Department of Mathematics
515 Loudon Road
Loudonville, NY 12211
United States