Some remarks regarding the $(p,q)-$Fibonacci and Lucas octonion polynomials

Math Methods in App Sciences

2021

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 different type of binomial transform.

Section: Discussionmentioning

confidence: 99%

On the binomial transforms of the Horadam quaternion sequences

Kaplan

Math Methods in App Sciences

2021

On Generalized Tribonacci Octonions

Sakarya University Journal of Science

2019

Self Cite

Generating functions for generalized tribonacci and generalized tricobsthal polynomials

Özmen

2022

Malaya J. Mat.

In this work, we consider generating functions which are generalized tribonacci polynomials Tn(x) and generalized tricobsthal polynomials Jn(x) which are defined in [7]. We derive generating functions for (m + n) − th order of generalized tribonacci polynomials and generalized tricobsthal polynomials for m ≥ 2. Furthermore, we obtain various families of bilinear and bilateral generating functions and give their special cases for these polynomials. Also, we obtain the summation formula of generalized tribonacci polynomials and generalized tricobsthal polynomials.