On Higher Order Jacobsthal Hyper Complex Numbers
Year: 2024
Type: article
Abstract: In this work, we define a new class of hyper complex numbers whose components are higher order Jacobsthal numbers, and call such numbers as the higher order Jacobsthal $ 2^{s} $-ions. We obtain some algebraic properties of the higher order Jacobsthal $ 2^{s} $-ions such as recurrence relation, Binet-like formula, generating function, exponential generating function, Vajda's identity, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity. Morever we derive the matrix representation of the higher order Jacobsthal $ 2^{s} $-ions, and so prove Cassini's identity as a further type.
Author: Hayrullah Özimamoğlu
Institution: Nevşehir Hacı Bektaş Veli University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4399441972