On a New Generalization of Pell Hybrid Numbers

Abstract

In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r-Pell numbers, we define the r-Pell hybrid numbers. We give their properties: character, Binet formula, summation formula, and generating function. Moreover, we present Catalan, Cassini, d’Ocagne, and Vajda type identities for the r-Pell hybrid numbers.

Keywords

• recurrence relations
• complex numbers
• hyperbolic numbers
• dual numbers
• hybrid numbers
• pell hybrid numbers
• 11b37
• 11b39