PreprintCC BY 4.0arXiv
Multiple harmonic star sums involving central binomial coefficients as weights
Abstract
We consider weighted analogues of multiple harmonic and multiple t-harmonic star sums, where the "star" indicates non-strict inequalities between the summation indices. In the special case where all exponents are 2, which is of particular interest also for ordinary multiple (t-)harmonic star sums, we obtain evaluations in terms of simple finite sums. The proofs are based on several combinatorial identities which are of interest in their own right.
Related
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BibTeX
@misc{dilcher2026multiple,
title = {{Multiple harmonic star sums involving central binomial coefficients as weights}},
author = {Karl Dilcher and Christophe Vignat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35021},
eprint = {2610.35021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35021},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multiple harmonic star sums involving central binomial coefficients as weights
AU - Karl Dilcher
AU - Christophe Vignat
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35021
UR - https://arxiv.org/abs/2610.35021
AB - We consider weighted analogues of multiple harmonic and multiple t-harmonic star sums, where the "star" indicates non-strict inequalities between the summation indices. In the special case where all exponents are 2, which is of particular interest also for ordinary multiple (t-)harmonic star sums, we obtain evaluations in terms of simple finite sums. The proofs are based on several combinatorial identities which are of interest in their own right.
ER -