More Fibonacci-Bernoulli relations with and without balancing polynomials

2020/07/29 by Robert Frontczak, Taras Goy, Frontczak, Robert +1
Mathematics · Physics and Astronomy · #05A15 #11B37 #11B65 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.14618

openalex publication_date 2020/07/29 · openalex created_date 2020/08/03 · openalex updated_date 2026/07/28

Abstract

We continue our study on relationships between Bernoulli polynomials and balancing (Lucas-balancing) polynomials. From these polynomial relations, we deduce new combinatorial identities with Fibonacci (Lucas) and Bernoulli numbers. Moreover, we prove a special identity involving Bernoulli polynomials and Fibonacci numbers in arithmetic progression. Special cases and some corollaries will highlight interesting aspects of our findings. Our results complement and generalize these of Frontczak (2019).

Related

• Lucas-Euler relations using balancing and Lucas-balancing polynomials
• Additional Fibonacci-Bernoulli relations
• Additional close links between balancing and Lucas-balancing polynomials
• Balancing polynomials, Fibonacci numbers and some new series for π
• Identities for Fibonacci and Lucas polynomials derived from a book of Gould