Year: 2024
Type: preprint
Abstract: This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negative even integers are found and Laurent expansions at poles are described. Closed-form expressions are derived for the Stieltjes constants that occur in Laurent expansions in a neighborhood of s=1. Moreover, as a bonus, it is obtained that the values at the positive odd integers of three harmonic zeta functions can be expressed in closed-form evaluations in terms of zeta values and log-sine integrals.
Source: arXiv (Cornell University)
Institution: Akdeniz University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4392781752