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ON THE BINOMIAL TRANSFORMS OF THE HORADAM QUATERNION SEQUENCES
  • Faruk Kaplan,
  • Arzu Özkoç Öztürk
Faruk Kaplan
Duzce University
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Arzu Özkoç Öztürk
Düzce Üniversitesi
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Abstract

The main object of the present paper is to consider the binomial transforms for Horadam quaternion sequences. We gave new formulas for recurrence relation, generating function, Binet formula and some basic identities for the binomial sequence of Horadam quaternions. Working with Horadam quaternions, we have found the most general formula that includes all binomial transforms with recurrence relation from the second order. In the last part, we determined the recurrence relation for this new type of quaternion by working with the iterated binomial transform, which is a dierent type of binomial transform.

Peer review status:ACCEPTED

30 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
03 Dec 2020Submission Checks Completed
03 Dec 2020Assigned to Editor
08 Dec 2020Reviewer(s) Assigned
17 Jan 2021Review(s) Completed, Editorial Evaluation Pending
19 Jan 2021Editorial Decision: Revise Minor
22 Jan 20211st Revision Received
23 Jan 2021Submission Checks Completed
23 Jan 2021Assigned to Editor
24 Jan 2021Reviewer(s) Assigned
27 Jan 2021Review(s) Completed, Editorial Evaluation Pending
09 Feb 2021Editorial Decision: Accept