On (p, q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums

Abstract

Formulas and sums involving many well-known special quaternion sequences (such as the Fibonacci, Pell, Jacobsthal quaternion sequences and so on) play important roles in various branches of science. Binet formulas, generating functions and certain sums of these quaternion sequences based on Fibonacci-like numbers have been investigated by a number of authors in many different ways. In this paper, which is a sequel to earlier works, we first introduce a new class of (p, q)-Fibonacci quaternions which generalizes Fibonacci, Pell, and Jacobsthal quaternions, and then we derive a new Binet formula, generating functions, and certain binomial sums for these quaternions.