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.

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.

$\mathrm{with}\left(\mathrm{OrthogonalSeries}\right)\:$

$\mathrm{Create}\left(u\left(n\right)\,\mathrm{HermiteH}\left(n\,x\right)\right)$

$\sum _{n=0}^{\mathrm{\infty }}u\left(n\right)\mathrm{HermiteH}\left(n\,x\right)$

$C≔\mathrm{ChangeBasis}\left(1+3y{x}^2+y^{3}x\,\mathrm{ChebyshevT}\left(n\,x\right)\,\mathrm{ChebyshevU}\left(m\,y\right)\right)$

$C≔\mathrm{ChebyshevT}\left(0\,x\right)\mathrm{ChebyshevU}\left(0\,y\right)+\frac{3\mathrm{ChebyshevT}\left(0\,x\right)\mathrm{ChebyshevU}\left(1\,y\right)}{4}+\frac{\mathrm{ChebyshevT}\left(1\,x\right)\mathrm{ChebyshevU}\left(1\,y\right)}{2}+\frac{3\mathrm{ChebyshevT}\left(2\,x\right)\mathrm{ChebyshevU}\left(1\,y\right)}{4}$

$\mathrm{Evaluate}\left(C\right)$

$3x^{2}y+yx+1$