Series and sums involving the floor function

2023/03/26 by Kunle Adegoke, Robert Frontczak, Adegoke, Kunle +3
Mathematics · Physics and Astronomy · #40A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Primary 11B39 #Secondary 11B37

paper · pdf · doi:10.48550/arxiv.2303.15478

openalex publication_date 2023/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (a_n)_{n≥ 0} be an arbitrary sequence and (a_{\lfloor n/k \rfloor})_{n≥ 0} its dual floor sequence. We study infinite series and finite generalized binomial sums involving (a_{\lfloor n/k \rfloor})_{n≥ 0}. As applications we prove a range of new closed form expressions for Fibonacci (Lucas) series and binomial sum identities as particular cases.

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