CAOP: Computer Algebra and Orthogonal Polynomials

CAOP is a package for calculating formulas for orthogonal polynomials belonging to the Askey scheme by Maple (at present Maple 11). With the present version users can compute recurrence relations, differential and difference equations or make a plot of every polynomial in the Askey scheme, without having Maple installed on their own computer. It is also possible to multiply the polynomial by a scaling function, to change the argument and to give values to the parameters by filling out a form, before doing the calculation. As an extra option the user can choose the layout of the output: prettyprint, lineprint or LaTeX. The latter two options make it possible to insert the output in another Maple worksheet respectively in a LaTeX document by a simple mouse-action.

Furthermore there are some help pages available for users who are not familiar with Maple. They can be viewed simultaneously while filling in the form.

Most computations in CAOP are performed by calling procedures in hsum10 (Package "Hypergeometric Summation", Maple 6-11, Copyright 1998-2006, Wolfram Koepf, University of Kassel).

The implementation of CAOP was originally done by René Swarttouw as part of the Askey-Wilson-Scheme Project performed at RIACA in Eindhoven. The present version is maintained by Wolfram Koepf.

There is work in progress to improve and extend CAOP.

If you want to use CAOP for polynomials in the Askey-scheme choose one of the following options:

If you want to use CAOP for polynomials in the q-Askey-scheme choose one of the following options:


Koepf, Wolfram and Swarttouw, René: "CAOP: Computer Algebra and Orthogonal Polynomials".

Last modified: Oct 8, 2007