On an Exact Relation between ? ?(2) and the Meijer G -Functions

Luis Acedo
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Luis Acedo: Instituto Universitario de Matemática Multidisciplinar, Building 8G, 2 o Floor, Camino de Vera, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2019, vol. 7, issue 4, 1-7

Abstract: In this paper we consider some integral representations for the evaluation of the coefficients of the Taylor series for the Riemann zeta function about a point in the complex half-plane ℜ ( s ) > 1 . Using the standard approach based upon the Euler-MacLaurin summation, we can write these coefficients as Γ ( n + 1 ) plus a relatively smaller contribution, ξ n . The dominant part yields the well-known Riemann’s zeta pole at s = 1 . We discuss some recurrence relations that can be proved from this standard approach in order to evaluate ζ ″ ( 2 ) in terms of the Euler and Glaisher-Kinkelin constants and the Meijer G -functions.

Keywords: Riemann zeta function; Euler-Maclaurin summation; Meijer ?-functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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