Mathematics (Apr 2025)

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

  • Nianliang Wang,
  • Ruiyang Li,
  • Takako Kuzumaki

DOI
https://doi.org/10.3390/math13091469
Journal volume & issue
Vol. 13, no. 9
p. 1469

Abstract

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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.

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