 OrthogonalSeries - Maple Help

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Overview of the OrthogonalSeries Package Calling Sequence OrthogonalSeries:-command(arguments) command(arguments) Description

 • The OrthogonalSeries package contains commands to manipulate series of classical orthogonal polynomials or, more generally, hypergeometric polynomials.
 • Each command in the OrthogonalSeries package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 • The long form, OrthogonalSeries:-command, is always available. The short form can be used after loading the package. List of OrthogonalSeries Package Commands

 The following is a list of available commands.

 To display the help page for a particular OrthogonalSeries commands, see Getting Help with a Command in a Package. Examples

 > $\mathrm{with}\left(\mathrm{OrthogonalSeries}\right):$
 > $\mathrm{Create}\left(u\left(n\right),\mathrm{HermiteH}\left(n,x\right)\right)$
 ${\sum }_{{n}{=}{0}}^{{\mathrm{\infty }}}{}{u}{}\left({n}\right){}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right)$ (1)
 > $C≔\mathrm{ChangeBasis}\left(1+3y{x}^{2}+{y}^{3}x,\mathrm{ChebyshevT}\left(n,x\right),\mathrm{ChebyshevU}\left(m,y\right)\right)$
 ${C}{≔}{\mathrm{ChebyshevT}}{}\left({0}{,}{x}\right){}{\mathrm{ChebyshevU}}{}\left({0}{,}{y}\right){+}\frac{{3}{}{\mathrm{ChebyshevT}}{}\left({0}{,}{x}\right){}{\mathrm{ChebyshevU}}{}\left({1}{,}{y}\right)}{{4}}{+}\frac{{\mathrm{ChebyshevT}}{}\left({1}{,}{x}\right){}{\mathrm{ChebyshevU}}{}\left({1}{,}{y}\right)}{{2}}{+}\frac{{3}{}{\mathrm{ChebyshevT}}{}\left({2}{,}{x}\right){}{\mathrm{ChebyshevU}}{}\left({1}{,}{y}\right)}{{4}}$ (2)
 > $\mathrm{Evaluate}\left(C\right)$
 ${3}{}{{x}}^{{2}}{}{y}{+}{y}{}{x}{+}{1}$ (3)