The ConvertToSum(S) function converts the orthogonal series S to a Maple sum.

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

$S≔\mathrm{Create}\left(u\left(n\right)\,\mathrm{ChebyshevT}\left(n\,x\right)\right)$

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

$\mathrm{lprint}\left(S\right)$

ORTHOGONALSERIES(array(0 .. 1,[(0)=(table(sparse,[("dim")=1,("table")=(table(sparse,[])),("bounds")=[0, infinity],("general")=u(n)])),(1)=(table([("index")=n,("variable")=x,("genre")=["ChebyshevT"]]))]))

$R≔\mathrm{ConvertToSum}\left(S\right)$

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

$\mathrm{lprint}\left(R\right)$

Sum(u(n)*ChebyshevT(n,x),n = 0 .. infinity)