On the Horadam symbol elements

TL;DR

This paper introduces Horadam symbol elements, explores their properties, and derives well-known identities like Catalan, Cassini, and d'Ocagne's for these new mathematical objects.

Contribution

The paper presents the concept of Horadam symbol elements and establishes several classical identities for them, expanding the understanding of their algebraic properties.

Findings

Derivation of Catalan identity for Horadam symbol elements

Establishment of Cassini formula for these elements

Proof of d'Ocagne's identity in this context

Abstract

Horadam symbol elemnts are introduced. Certain properties of these elements are explored. Some well known identities such as Catalan identity, Cassini formula and d'Ocagne's identity are obtained for these elements.