About Rec2ortho

Tom Koornwinder and René Swarttouw are writing together a procedure in Maple, called rec2ortho, which uses the coefficients of a three-term recurrence relation for orthogonal polynomials as input, and which returns the explicit system of OP's solving these recurrence relations, provided it belongs to the Askey scheme or q-Askey scheme. Eventually, this should also return associated OP's and other explicit OP's which are not in the (q-)Askey scheme. At the moment, the procedure only covers the OP's in the Askey scheme (q=1) up to the level of 2 parameters (Jacobi, Meixner, etc.). The procedue can be used in Maple 6, 7, 8 or 9.

The present version is 1b3 (completed on 16 July, 1998, for Maple V, Release 4 and 5, and tested on 19 March, 2005 for Maple 9). Compared to the first version (June 1996), many improvements have been made. Work on extending the coverage of classes of OP's is still in progress.

The following files are available:

rec2ortho (source code of the Maple procedure)
help_rec2ortho (help file)
rec2orthotest.mws (a Maple worksheet for Maple 6, 7, 8 with many examples)
rec2orthotest.mw (the same Maple worksheet for Maple 9)

The project will be continued by Tom Koornwinder alone. He welcomes questions, comments and suggestions about this project.

This work started as part of the larger project A computer implementation of the Askey-Wilson scheme, on which René Swarttouw worked during the period January 1 - July 1, 1996 at RIACA, Eindhoven.

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