Shifted quadratic Zeta series

Anthony Sofo

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-22

Abstract:

It is well known that the Riemann Zeta function ς ( p ) = ∑ n = 1 ∞ 1 / n p can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑ n = 1 ∞ 1 / ( 4 n 2 − α 2 ) p . In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form representations of alternating sign shifted quadratic Zeta series.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:756202

DOI: 10.1155/S0161171204402026

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