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
Scientific Journal Rankings
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