- Hypergeometric Orthogonal Polynomials and Their q-Analogues
- NIST Handbook and Digital Library of Mathematical Functions
- The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
- Differential equations for generalized Laguerre and Jacobi polynomials
- Generalizations of the classical Laguerre polynomials and some q-analogues
- List of publications
- List of technical reports
- List of co-workers
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Faculty of Information Technology and Systems
Department of Technical Mathematics and Informatics
Report no. 98-17
In 1994 the first (preliminary) version of the report
Roelof Koekoek and René F. Swarttouw: The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Delft University of Technology, Faculty of Technical Mathematics and Informatics, Report no. 94-05, 1994.appeared. In 1996 we published an updated version in which we only corrected some misprints in the original (1994) report.
During the first half of 1996 René worked on the projectTom H. Koornwinder and is part of the project Human Interaction with Symbolic Computation (HISC) at the Research Institute for Applications of Computer Algebra (RIACA).
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.You may download the report by clicking the red number above.
This revised version contained a description of all families of hypergeometric orthogonal polynomials appearing in the Askey-scheme (named after Richard A. Askey) and in the q-analogue of this scheme. For all families of these (basic) hypergeometric orthogonal polynomials we gave
and also the (limit) relations between the families of orthogonal polynomials appearing in both schemes. Further we updated the list of references and added the following formulas for each family of (basic) hypergeometric orthogonal polynomials:
- the definition in terms of hypergeometric functions - the orthogonality relation - the three term recurrence relation - the second order differential or difference equation - some generating functions
- the three term recurrence relation for the monic orthogonal polynomials (with leading coefficient equal to 1) - forward and backward shift operators - Rodrigues-type formula
For questions or comments concerning the report please contact either
Roelof Koekoek (e-mail: R.Koekoek@TUDelft.NL) or René F. Swarttouw (e-mail: email@example.com).
This picture was taken by Herman Bavinck in Toronto (1995)
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Last modified on January 2, 2013