Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials
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Date
2006
Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
TAYLOR & FRANCIS LTD
Series Info
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS;Volume: 17 Issue: 5 Pages: 329-353
Scientific Journal Rankings
Abstract
Two formulae expressing explicitly the difference derivatives and the moments of a discrete orthogonal polynomials {P-n(x): Meixner, Kravchuk and Charlier} of any degree and for any order in terms of P-n(x) themselves are proved. Two other formulae for the expansion coefficients of a general-order difference derivatives del(q) f(x), and for the moments x(l)del(q) f(x), of an arbitrary function f (x) of a discrete variable in terms of its original expansion coefficients are also obtained. Application of these formulae for solving ordinary 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 two families of Meixner, Kravchuk and Charlier, is described. Three analytical formulae for the connection coefficients between Hahn-Charlier, Hahn-Meixner and Hahn-Kravchuk are also developed.
Description
Accession Number: WOS:000238564600003
Keywords
University for Hahn, Meixner, Kravchuk and Charlier polynomials, expansion coefficients recurrence, relations, linear difference equations, connection coefficients
Citation
Cited References in Web of Science Core Collection: 33