Article ID: MTJPAM-D-24-00005

Title: Series and sums involving the floor function


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00005; Volume 8 / Issue 2 / Year 2026, Pages 1-26

Document Type: Research Paper

Author(s): Kunle Adegoke a, Robert Frontczak b, Taras Goy c

aDepartment of Physics and Engineering Physics, Obafemi Awolowo University, 220005 Ile-Ife, Nigeria

bIndependent Researcher, 72764 Reutlingen, Germany

cFaculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 76018 Ivano-Frankivsk, Ukraine

Received: 10 January 2024, Accepted: 2 December 2025, Published: 4 June 2026

Corresponding Author: Taras Goy (Email address: taras.goy@pnu.edu.ua)

Full Text: PDF

Abstract

Let (an)n ≥ 0 be an arbitrary sequence and (a⌊n/k⌋)n ≥ 0 its dual floor sequence. We study infinite series and finite generalized binomial sums involving (a⌊n/k⌋)n ≥ 0. As applications, we prove a range of new closed-form expressions for the Fibonacci (Lucas) series and binomial sum identities as particular cases.

Keywords: Floor function, power series, generating function, binomial transform, Fibonacci (Lucas) number, Gibonacci sequence

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Cite this article

How to cite this article: K. Adegoke, R. Frontczak and T. Goy, Series and sums involving the floor function, Montes Taurus J. Pure Appl. Math. 8 (2), 1-26, 2026; Article ID: MTJPAM-D-24-00005.