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 -