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Four Variants of Riemann Zeta Function

Author

Listed:
  • Nadia N. Li

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Wenchang Chu

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
    Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

Abstract

By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in closed form, which shows remarkably that the values of these series result in multiples of integer powers of π either by rational numbers or by algebraic numbers.

Suggested Citation

  • Nadia N. Li & Wenchang Chu, 2022. "Four Variants of Riemann Zeta Function," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2992-:d:892213
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