Classification of hypergeometric orthogonal polynomials

Together with Peter A. Lesky and René F. Swarttouw I have been working on a classification of orthogonal polynomials belonging to the Askey scheme of hypergeometric orthogonal polynomials and their q-analogues.

We started with second-order differential and difference equations and looked for polynomial solutions. This lead to three-term recurrence relations. Then the theorem of Favard gave us conditions for the existence of orthogonal polynomial solutions. The orthogonality measures or functionals can be obtained by using the Pearson differential equation and the Rodrigues formula.

Our goal was to combine the preprints

Peter A. Lesky : Eine Charakterisierung der kontinuierlichen und diskreten klassischen Orthogonalpolynome. Universität Stuttgart, Mathematisches Institut A, Preprint no. 98-12, 1998

See also:

Peter A. Lesky : Eine Charakterisierung der klassischen kontinuierlichen-, diskreten- und q-Orthogonalpolynome, Shaker Verlag, Aachen, 2005, ISBN 3-8322-3796-8

and

Roelof Koekoek and René F. Swarttouw : The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Delft University of Technology, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics, Report no. 98-17, 1998

See also the online version.

Eventually this work has lead to the book Hypergeometric Orthogonal Polynomials and Their q-Analogues.

Last modified on November 11, 2009

• Home Home
• Education Education
• Research Research
  • Hypergeometric Orthogonal Polynomials and Their q-Analogues Hypergeometric Orthogonal Polynomials and Their q-Analogues
  • Classification of hypergeometric orthogonal polynomials Classification of hypergeometric orthogonal polynomials
  • NIST Digital Library of Mathematical Functions NIST Digital Library of Mathematical Functions
  • The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
  • Differential equations for generalized Laguerre and Jacobi polynomials Differential equations for generalized Laguerre and Jacobi polynomials
  • Generalizations of the classical Laguerre polynomials and some q-analogues Generalizations of the classical Laguerre polynomials and some q-analogues
  • List of publications List of publications
  • List of technical reports List of technical reports
• List of co-workers List of co-workers