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Research Article Open access CC BY 4.0

Generalized Horadam-Leonardo Numbers and Polynomials

Yüksel Soykan

Asian Journal of Advanced Research and Reports · pp. 128–169 · Published 5 Jun 2023

10.9734/ajarr/2023/v17i8511

Abstract

In this study, we define and investigate some linear third order polynomials called the generalized Horadam-Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sum formulas for these polynomial sequences. Also, we present some identities and matrices related to these polynomials. Furthermore, we present some special cases of generalized Horadam-Leonardo polynomials, namely, generalized Leonardo, generalized John, generalized Ernst, generalized Pisano, generalized Edouard and generalized Bigollo numbers.

Horadam polynomials fibonacci polynomials tribonacci polynomials horadam-leonardo polynomials third order recurrence relations

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