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2010 $\zeta(n)$ via hyperbolic functions
Joseph D’Avanzo, Nikolai Krylov
Involve 3(3): 289-296 (2010). DOI: 10.2140/involve.2010.3.289

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.

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Joseph D’Avanzo. Nikolai Krylov. "$\zeta(n)$ via hyperbolic functions." Involve 3 (3) 289 - 296, 2010. https://doi.org/10.2140/involve.2010.3.289

Information

Received: 13 November 2009; Accepted: 29 June 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1253.26019
MathSciNet: MR2739520
Digital Object Identifier: 10.2140/involve.2010.3.289

Subjects:
Primary: 26B15
Secondary: 11M06

Rights: Copyright © 2010 Mathematical Sciences Publishers

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