On Higher Order Jacobsthal Hyper Complex Numbers

Authors : Hayrullah Özimamoğlu

Pages : 35-44

Doi:10.47000/tjmcs.1195463

View : 68 | Download : 90

Publication Date : 2024-06-30

Article Type : Research Paper

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.
Keywords : Hyper complex numbers, higher order Jacobsthal numbers, higher order Jacobsthal 2^ s ions, Binet like formula, recurrence relation