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

Nianliang Wang (), Ruiyang Li and Takako Kuzumaki ()
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Nianliang Wang: School of Applied Mathematics and Computer Science, Institute of Applied Mathematics, Shangluo University, Shangluo 726000, China
Ruiyang Li: School of Applied Mathematics and Computers, Xi’an Technological University, Xi’an 710064, China
Takako Kuzumaki: Department of Mathematics, Faculty of Engineering, Gifu University, Gifu 501-1193, Japan

Mathematics, 2025, vol. 13, issue 9, 1-12

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.

Keywords: Riemann zeta-function; Hurwitz zeta-function; integral representation for partial sums; functional equation; special values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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