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

Instituto Universitario de Matemática Multidisciplinar, Building 8G, 2o Floor, Camino de Vera, Universitat Politècnica de València, 46022 Valencia, Spain
Mathematics 2019, 7(4), 371; https://doi.org/10.3390/math7040371
Received: 25 March 2019 / Revised: 12 April 2019 / Accepted: 15 April 2019 / Published: 24 April 2019
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 ( 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. View Full-Text
Keywords: Riemann zeta function; Euler-Maclaurin summation; Meijer ?-functions Riemann zeta function; Euler-Maclaurin summation; Meijer ?-functions
MDPI and ACS Style

Acedo, L. On an Exact Relation between ζ″(2) and the Meijer G -Functions. Mathematics 2019, 7, 371.

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