- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 69 Issue: 1
- A note on hyperbolic (p,q)-Fibonacci quaternions
A note on hyperbolic (p,q)-Fibonacci quaternions
Authors : Tülay Yağmur
Pages : 880-890
Doi:10.31801/cfsuasmas.582674
View : 7 | Download : 7
Publication Date : 2020-06-30
Article Type : Research
Abstract :In this paper, we introduce a new quaternion sequence called hyperbolic (p,q)-Fibonacci quaternions. This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic Pell, hyperbolic k-Pell, hyperbolic Jacobsthal, hyperbolic k-Jacobsthal quaternions. We give generating function and Binet formula for these quaternions. We also obtain some identities such as d'Ocagne's, Catalan's and Cassini's identities involving hyperbolic (p,q)-Fibonacci quaternions.Keywords : Fibonacci numbers, (p, q)-Fibonacci numbers, (p, q)-Fibonacci quaternions, hyperbolic quaternions, hyperbolic (p, q)-Fibonacci quaternions