PreprintCC BY 4.0arXiv
On the Euler transform and the floor function
Abstract
Let (an)n≥ 0 be a sequence of numbers. We derive an expression for the Euler transform of a general binomial sum involving an and weighted by the floor function. To demonstrate the usefulness of our approach, several examples are discussed. We rediscover some known identities and prove several new. In particular, we derive some new identities for weighted binomial sums involving harmonic numbers and central binomial coefficients. We also present new closed-forms for weighted series involving the Riemann zeta function.
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BibTeX
@misc{frontczak2026euler,
title = {{On the Euler transform and the floor function}},
author = {Robert Frontczak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25190},
eprint = {2609.25190},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25190},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Euler transform and the floor function
AU - Robert Frontczak
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25190
UR - https://arxiv.org/abs/2609.25190
AB - Let (a_n)_n≥ 0 be a sequence of numbers. We derive an expression for the Euler transform of a general binomial sum involving a_n and weighted by the floor function. To demonstrate the usefulness of our approach, several examples are discussed. We rediscover some known identities and prove several new. In particular, we derive some new identities for weighted binomial sums involving harmonic numbers and central binomial coefficients. We also present new closed-forms for weighted series involving the Riemann zeta function.
ER -