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Partial Sums of the Hurwitz and Allied Functions and Their Special Values

Author

Listed:
  • Nianliang Wang

    (School of Applied Mathematics and Computer Science, Institute of Applied Mathematics, Shangluo University, Shangluo 726000, China
    These authors contributed equally to this work.)

  • Ruiyang Li

    (School of Applied Mathematics and Computers, Xi’an Technological University, Xi’an 710064, China
    These authors contributed equally to this work.)

  • Takako Kuzumaki

    (Department of Mathematics, Faculty of Engineering, Gifu University, Gifu 501-1193, Japan)

Abstract

We supplement the formulas for partial sums of the Hurwitz zeta-function and its derivatives, producing more integral representations and generic definitions of important constants. Then, these are used, coupled with the functional equation for the completed zeta-function to clarify the results of Choudhury, giving rise to closed expressions for the Riemann zeta-function and its derivatives.

Suggested Citation

  • Nianliang Wang & Ruiyang Li & Takako Kuzumaki, 2025. "Partial Sums of the Hurwitz and Allied Functions and Their Special Values," Mathematics, MDPI, vol. 13(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1469-:d:1646114
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