A set of orthogonal polynomials, dual to alternative q-Charlier polynomials

نویسنده

  • Natig M. Atakishiyev
چکیده

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 three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also established. Mathematical Subject Classification (2000): 33D45, 47B36, 81Q10

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalization of matching extensions in graphs-combinatorial interpretation of orthogonal and q-orthogonal polynomials

In this paper, we present generalization of matching extensions in graphs and we derive combinatorial interpretation of wide classes of orthogonal and q-orthogonal polynomials. Specifically, we assign general weights to complete graphs, cycles and chains or paths defining matching extensions in these graphs. The generalized matching polynomials of these graphs have recurrences defining various ...

متن کامل

Exceptional Charlier and Hermite orthogonal polynomials

Using Casorati determinants of Charlier polynomials (ca n )n , we construct for each finite set F of positive integers a sequence of polynomials cF n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF ( N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials cF n , n ∈ σF , a...

متن کامل

. C A ] 9 J ul 1 99 3 The q - Harmonic Oscillator and an Analog of the Charlier polynomials

A model of a q-harmonic oscillator based on q-Charlier poly-nomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an ana-log of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed. Models of q-harmonic oscillators are being develop...

متن کامل

Linearization coefficients for orthogonal polynomials using stochastic processes

ABSTRACT. Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical families of orthogonal polynomials. Starting with a stochastic process and using the stochastic measures machinery introduced by Rota and Wallstrom...

متن کامل

DUAL PROPERTIES OF ORTHOGONAL POLYNOMIALS OF DISCRETE VARIABLES ASSOCIATED WITH THE QUANTUM ALGEBRA Uq(su(2))

We show that for every set of discrete polynomials yn(x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials zk(ξ(t)) of degrees k = s−a and k = b− s− 1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative f...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003