Higher-Order Jacobsthal–Lucas Quaternions

Abstract

In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties. We give Binet’s formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, and exponential generating functions of the higher-order Jacobsthal–Lucas quaternions. We also give some relations between higher-order Jacobsthal and Jacobsthal–Lucas quaternions.

Keywords

• Jacobsthal–Lucas quaternions
• higher-order Jacobsthal–Lucas quaternions
• Binet formula