Year: 2026
Type: preprint
Abstract: Let $(a_n)_{n\geq 0}$ 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.
Source: arXiv (Cornell University)
Author: Frontczak, Robert
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214091759