This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Open AccessArticle
Partial Sums of the Hurwitz and Allied Functions and Their Special Values
by
Nianliang Wang
Nianliang Wang
,
Ruiyang Li
Ruiyang Li
Takako Kuzumaki
Takako Kuzumaki
Takako Kuzumaki Kobayashi is Professor at Gifu University. She completed her PhD studies in at She [...]
Takako Kuzumaki Kobayashi is Professor at Gifu University. She completed her PhD studies in Mathematics at Kyushu University. She published 25 papers in various journals and two books. She is teaching the disciplines of basic algebra and analysis and cryptograms. Her interests include Algebraic Number Theory and Analytic Number Theory.
1
School of Applied Mathematics and Computer Science, Institute of Applied Mathematics, Shangluo University, Shangluo 726000, China
2
School of Applied Mathematics and Computers, Xi’an Technical University, Xi’an 726000, China
3
Faculty of Engineering, Department of Mathematics, Gifu University, Gifu 501-1193, Japan
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2025, 13(9), 1469; https://doi.org/10.3390/math13091469 (registering DOI)
Submission received: 26 February 2025
/
Revised: 8 April 2025
/
Accepted: 24 April 2025
/
Published: 29 April 2025
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.
Share and Cite
MDPI and ACS Style
Wang, N.; Li, R.; Kuzumaki, T.
Partial Sums of the Hurwitz and Allied Functions and Their Special Values. Mathematics 2025, 13, 1469.
https://doi.org/10.3390/math13091469
AMA Style
Wang N, Li R, Kuzumaki T.
Partial Sums of the Hurwitz and Allied Functions and Their Special Values. Mathematics. 2025; 13(9):1469.
https://doi.org/10.3390/math13091469
Chicago/Turabian Style
Wang, Nianliang, Ruiyang Li, and Takako Kuzumaki.
2025. "Partial Sums of the Hurwitz and Allied Functions and Their Special Values" Mathematics 13, no. 9: 1469.
https://doi.org/10.3390/math13091469
APA Style
Wang, N., Li, R., & Kuzumaki, T.
(2025). Partial Sums of the Hurwitz and Allied Functions and Their Special Values. Mathematics, 13(9), 1469.
https://doi.org/10.3390/math13091469
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details
here.
Article Metrics
Article Access Statistics
For more information on the journal statistics, click
here.
Multiple requests from the same IP address are counted as one view.
