Horadam-Lagrange Interpolation Polynomials: Construction, Recurrence Relations, and Connections to Special Number Sequences

Orhan Diskaya

doi:10.61383/ejam.20253195

Authors

Orhan Diskaya Department of Mathematics, Mersin University, Mersin 33343, Turkey https://orcid.org/0000-0001-5698-7834

DOI:

https://doi.org/10.61383/ejam.20253195

Keywords:

Fibonacci numbers, Horadam numbers, Lagrange interpolation polynomials

Abstract

This study investigates the construction of polynomials of at most degree \(n\) using the first \(n+1\) terms of the Horadam sequence through Lagrange interpolation. The paper provides a comprehensive analysis of the recurrence relations and fundamental identities associated with the Horadam-Lagrange Interpolation Polynomials. Furthermore, it explores the structural properties and special cases of these polynomials, highlighting their connections to well-known sequences such as Fibonacci, Lucas, Pell, Jacobsthal, Mersenne and Fermat sequences.

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