This code provides tools to help compute linear recurrences for coefficients of generalized Fourier expansions in a basis of classical orthogonal polynomials.

Latest version

GeneralizedFourierSeries 1.0 (May 2026).

This file is meant to be read by Maple (using the command read). It can also be read by anyone who can read Maple code.

Examples

With input the following function:

F:=sin(2*a*x)/x;

The command

FunctiontoRec(F,HermiteH(k,x),u);

produces the output \[ a^{2} u_k+(2+k) (2 a^{2}+k+3)u_{k+2}+2 (2+k)(3+k) (4+k) u_{k+4} \] which is a recurrence operator that annihilates the coefficients \(u_k\) in the expansion

\[\frac{\sin 2ax}x=\sum_{k=0}^\infty u_kH_k(x).\]

A Maple worksheet of examples is available, also in pdf.

Reference for the package

This package was designed to illustrate the approach in

(missing reference)

Bugs

If you see any problem when using this package, please send me an email at bruno.salvy@inria.fr.