Related papers: Unrestricted modified third-order Jacobsthal quate…
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality…
In this paper, we study a generalization of Jacobsthal and Jacobsthal-Lucas numbers, we find their generating function binet formulas, related matrix representation and many other properties
Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…
In this paper, we deal with two families of third-order Jacobsthal sequences. The first family consists of generalizations of the Jacobsthal sequence. We show that the Gelin-Ces\`aro identity is satisfied. Also, we define a family of…
In this paper, a new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A Vadja formula for the generalized bihyperbolic third-order Jacobsthal…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many different ways. In addition, formulas and identities involving these…
An algebra A not encountered in either the usual algebraic varieties or supervarieties is introduced. A is a graded and deformed version of the quaternions, with structure similar to that of a Jordan-Lie superalgebra as defined by Okubo and…
In this note, we give a concrete realization of the Jacquet-Langlands correspondence for non-Eichler orders of indefinite quaternion algebras defined over $\mathbb Q$. To be more precise, we consider a special type of index-two suborder of…
This study applies the binomial, k-binomial, rising k-binomial and falling k-binomial transforms to the modified k-Fibonacci-like sequence. Also, the Binet formulas and generating functions of the above mentioned four transforms are newly…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Let $\F$ be the finite field of odd prime power order $q$, We find explicit expressions for the number of triples $\{\al-1,\al,\al+1 \}$ of consecutive non-zero squares in $\F$ and similarly for the number of triples of consecutive…
We show how to construct unramified qoaternion extensions of quadratic number fields.
In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.
Spinors are used in physics quite extensively. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined…
In this paper, we introduce the Tribonacci and Tribonacci-Lucas quaternion polynomials. We obtain the Binet formulas, generating functions and exponential generating functions of these quaternions. Moreover, we give some properties and…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
New regularities found in the pseudoscalar meson octet are reported. They invite to reconsider models where elementary fermions and composite QCD open strings can be grouped in common supermultiplets. It is proven that, with fermions having…
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…
We give combinatorial descriptions of the terms occurring in continuants of general continued fractions that diverge to three limits. Equating these with the usual combinatorial descriptions due to Euler, Sylvester, and Minding induces…