TY - JOUR

T1 - EXPLICIT EXPRESSIONS FOR SOME LINEAR EULER–TYPE SUMS CONTAINING HARMONIC AND SKEW–HARMONIC NUMBERS

AU - Stewart, Sean M.

N1 - KAUST Repository Item: Exported on 2023-07-24

PY - 2022

Y1 - 2022

N2 - Closed-form expressions for the three general linear Euler-type sums containing the harmonic numbers Hn and the skew-harmonic numbers Hn ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , ∞ ∑ n=1 Hn (2n+1)q , and ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , where q is a positive integer greater than or equal to zero or two as needed to ensure convergence are given. Closed-form expressions for several other closely related generalised logarithmic integrals and sums are also presented.

AB - Closed-form expressions for the three general linear Euler-type sums containing the harmonic numbers Hn and the skew-harmonic numbers Hn ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , ∞ ∑ n=1 Hn (2n+1)q , and ∞ ∑ n=1 (−1)nHn (2n+1)2q+1 , where q is a positive integer greater than or equal to zero or two as needed to ensure convergence are given. Closed-form expressions for several other closely related generalised logarithmic integrals and sums are also presented.

UR - http://hdl.handle.net/10754/693178

UR - http://jca.ele-math.com/20-07

UR - http://www.scopus.com/inward/record.url?scp=85164502563&partnerID=8YFLogxK

U2 - 10.7153/jca-2022-20-07

DO - 10.7153/jca-2022-20-07

M3 - Article

SN - 1848-5987

VL - 20

SP - 79

EP - 101

JO - Journal of Classical Analysis

JF - Journal of Classical Analysis

IS - 2

ER -