Related papers: Orthogonal polynomials and deformed oscillators
We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of Bernoulli polynomials, making use of the connection between…
Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this…
This article discuss a class of tractable model in the form of polynomial type.
The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek…
We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's…
Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…
The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of…
In this paper we describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.
We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any…
We prove recurrence relations and modulo periodic properties of multiple derivatives of Fibonacci polynomials. We apply the obtained results to present the dynamic structures of Fibonacci polynomials over the ring of 2-adic integers by…
The aim of this paper is to study a Lie conformal algebra of Block type. In this paper, conformal derivation, conformal module of rank 1 and low-dimensional comohology of the Lie conformal algebra of Block type are studied. Also, the vertex…
The oscillator algebra of Pegg-Barnett (P-B) oscillator with a finite-dimensional number-state space is investigated in this note. It is shown that the Pegg-Barnett oscillator possesses the su($n$) Lie algebraic structure. Additionally, we…
The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a…
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
An attempt had been made to get algebraic structure of 2D complex harmonic oscillator.
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
We study the Schroedinger equation for an off-diagonal tight-binding hamiltonian, as well as the equations of motion for out-of-plane vibrations, on the separable square Fibonacci quasicrystal. We discuss the nature of the spectra and wave…