Some identities deriving from the nth power of a special matrix

In this paper, we consider the Horadam sequence and some summation formulas involving the terms of the Horadam sequence. We derive combinatorial identities by using the trace, the determinant and the n th power of a special matrix

Some sums formulae for products of terms of Pell, Pell-Lucas and Modified Pell sequences

Özet Pell, Pell-Lucas ve Modified Pell dizilerinin terimleri için bazı toplam formüllerini elde ettik. Ayrıca, bu toplamların bu dizilerin terimlerine göre yazılabileceğini de gösterdik. Abstract We derive some sums formulae for certain products of terms of the Pell , Pell-Lucas and modified Pell sequences. Also, we show that these sums can be rewritten in terms of these sequences

On bicomplex polynomials

In this study, we examine polynomials with bicomplex coefficient and bicomplex variables. We investigate the roots of bicomplex polynomials by idempotent bases of bicomplex numbers and classified these roots. © 2018 Author(s)

On Some Bicomplex Hartley Transformations

In this study, we have defined Hartley transforms for functions of bicomplex variables by using some known integral transformations, and then we examined the properties of these transformations

On Fibonacci quaternion matrix

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini's identity using this new matrix.Scientific Research Coordination unit of Pamukkale University [2020KRM005-109]This study was supported by Scientific Research Coordination unit of Pamukkale University under the project number 2020KRM005-109

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients. Using the Binet form we prove fundamental relations between these numbers. Moreover, we investigate whether the quaternions newly defined provide existing some important identities such as Cassini's identity for quaternions

PADE YAKLAŞlMLARI

Yapılan bu çalışmada, bir formal kuvvet serisiyardımıyla bir fonksiyona nasıl yaklaşılabileceğiçalışıldı. Bir fonksiyona yaklaşabilmenin birçokyolları vardır. Pa de ve Pade tipi yaklaşımlarıbunlardan bazılarıdır. B u yaklaşımlar birer rasyonelyaklaşım olduklarından, rasyonel yaklaşımlarınözelliklerini taşırlar. Bu yaklaşım tipinin gösterimi,hesaplanışı ve hatasının bulunması, farklı şekillerdegösterimi ç alışıldı. Enterpotasyon polinomları ilebağlantıları anlatılarak, bu yaklaşırnların tek ve çokdeğişkenli durumları da incelendi

On a Study of (s; t)-Generalized Pell Sequence and its Matrix Sequence

First of all in this article, we consider (s; t)-type sequences suchas (s; t)-Pell sequence hPn (s; t)i, (s; t)-Pell-Lucas sequence hQn (s; t)iand (s; t)-Modified Pell sequence hRn (s; t)i. Also we consider (s; t)-type matrix sequences such as (s; t)-Pell matrix sequence hUn (s; t)i, (s; t)-Pell-Lucas matrix sequence hVn (s; t)i and (s; t)-Modified Pell matrix sequencehWn (s; t)i. Then we introduce (s; t)-generalized Pell sequencehTn (s; t)i and its matrix sequence named (s; t)-generalized Pell matrixsequence hXn (s; t)i. But the main aim here to present many new resultsfor (s; t)-generalized Pell sequence and (s; t)-generalized Pell matrix sequenceand study the relations for (s; t)-generalized Pell sequence and(s; t)-generalized Pell matrix sequence with other (s; t)-type sequencesand (s; t)-type matrix sequences. In addition to this we also define matrixsequences to (s; t)-type matrix sequences