2023/04/23 by Vincent Nguyen, Nguyen, Vincent
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2304.11614
openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
In this paper, we evaluate in closed form several different series involving the harmonic numbers and skew-harmonic numbers. We consider two classes of series involving these sequences. One class of series involves the product of the nth harmonic or skew-harmonic number and a tail. We provide the solution to two open problems concerning these harmonic series with tails from Ovidiu Furdui's book Sharpening Mathematical Analysis Skills. The other class of series is the Hardy series, which involves a logarithm and the Euler-Mascheroni constant being subtracted from the nth harmonic number.