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Bounds for Zeta and Related Functions

Cerone, Pietro (2005) Bounds for Zeta and Related Functions. Journal of Inequalities in Pure and Applied Mathematics, 6 (5). pp. 4-31. ISSN 1443-5756

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Abstract

Sharp bounds are obtained for expressions involving Zeta and related functions at a distance of one apart. Since Euler discovered in 1736 a closed form expression for the Zeta function at the even integers, a comparable expression for the odd integers has not been forthcoming. The current article derives sharp bounds for the Zeta, Lambda and Eta functions at a distance of one apart. The methods developed allow an accurate approximation of the function values at the odd integers in terms of the neighbouring known function at even integer values. The Dirichlet Beta function which has explicit representation at the odd integer values is also investigated in the current work. Cˇ ebyšev functional bounds are utilised to obtain tight upper bounds for the Zeta function at the odd integers.

Item Type: Article
Additional Information:

Article 134

Uncontrolled Keywords: ResPubID9342, Euler Zeta function, Dirichlet beta, eta and lambda functions, Sharp bounds, Cebyšev functional
Subjects: Faculty/School/Research Centre/Department > School of Engineering and Science
FOR Classification > 0199 Other Mathematical Sciences Information Systems
Depositing User: VUIR
Date Deposited: 28 Mar 2012 03:04
Last Modified: 28 Mar 2012 03:04
URI: http://vuir.vu.edu.au/id/eprint/2706
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Citations in Scopus: 1 - View on Scopus

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