In this study, we introduce a new family of Leonardo quaternions defined by means of quantum integers, which we call q-generalized Leonardo quaternions. The aim is to extend the previously introduced Leonardo quaternions and generalized Leonardo quate...
In this study, we introduce a new family of Leonardo quaternions defined by means of quantum integers, which we call q-generalized Leonardo quaternions. The aim is to extend the previously introduced Leonardo quaternions and generalized Leonardo quaternions. Furthermore, we derive several formulas and identities for this new family, including a Binet-like formula, exponential and Poisson generating functions, summation formulas, and Catalan-like, Cassini-like, and d’Ocagne-like identities.