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

Author

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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)

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.

Suggested Citation

  • Luis Acedo, 2019. "On an Exact Relation between ζ ″(2) and the Meijer G -Functions," Mathematics, MDPI, vol. 7(4), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:371-:d:225543
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