I would like to pay attention of the Maple Primes Users to a Sergey Moiseev application. This is a Maple package on orthogonal expansions, which can be implemented in Maple as a usual package with a usual help. It has Community Rating 4 stars. This package can be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=33406. Here is the list of its commands: with(OrthogonalExpansions);
[BesselSeries, ChebyshevTSeries, ChebyshevUSeries, FourierSeries,
GegenbauerSeries, GramSchmidtL2, Haar, HaarSeries, HarmonicWavelet,
HarmonicWaveletSeries, HermiteSeries, JacobiSeries, LaguerreSeries,
LegendreSeries, MixedSeries, Rational, RationalSeries, RectSeries,
SincSeries, SincWavelet, SincWaveletSeries, SphericalSeries, Walsh,
WalshSeries, Zernike, ZernikeSe]
It should be noted that the OrthogonalExpansions package includes the commands for Fourier multiseries and wavelets.