Original scientific paper

More Fibonacci-Bernoulli relations with and without balancing polynomials

Robert Frontczak orcid.org/0000-0002-9373-5297 ; Landesbank Baden-Württemberg, Stuttgart, Germany
Taras Goy ; Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, Ukraine

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).

Keywords

Bernoulli polynomials and numbers; balancing polynomials and numbers; Fibonacci numbers; Lucas numbers; generating function

Hrčak ID:

261515

URI

https://hrcak.srce.hr/261515

Publication date:

26.8.2021.

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