A note on hyperbolic (p,q)-Fibonacci quaternions
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Date
2020-06-30
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Ankara Üniversitesi Fen Fakültesi
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.
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Fibonacci numbers, (p;q)-Fibonacci numbers, (p;q)-Fibonacci quaternions