Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 346-351
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2023.0217
Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers
Parth Chavan\(^{1,*}\), Sarth Chavan\(^{1}\)
\(^{1}\) Euler Circle, Palo Alto, CA 94306, USA.
Copyright © 2023 Parth Chavan and Sarth Chavan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 29, 2023 – Accepted: August 11, 2023 – Published: December 27, 2023
Abstract
The main goal of this brief article is to provide an elementary proof of Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers.
Keywords:
Riemann zeta function; Catalans constant; Apéry-like sums; Harmonic numbers; Polylogarithm function; Polygamma function; Logarithmic integrals; Clausen function.