Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam-Carlitz I polynomials

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Date

2005

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

IOP PUBLISHING LTD

Series Info

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL;Volume: 38 Issue: 47 Pages: 10107-10121

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Abstract

Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives D-q(p) f(x), and for the moments x(e)D(q)(p) f (x), of an arbitrary function f (x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

Description

Accession Number: WOS:000233877900008

Keywords

University for CLASSICAL ORTHOGONAL POLYNOMIALS, INFINITELY DIFFERENTIABLE FUNCTION, TSCHEBYSCHEFF COEFFICIENTS, LINEARIZATION PROBLEM, HARMONIC-OSCILLATOR, LATTICE X(S)=Q(2S), JACOBI-POLYNOMIALS, Q-ANALOGS, DERIVATIVES, FORMULAS

Citation

ited References in Web of Science Core Collection: 58