OrthogonalSeries - Maple Programming Help

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OrthogonalSeries

 ConvertToSum
 convert a series to a Maple sum

 Calling Sequence ConvertToSum(S)

Parameters

 S - orthogonal series

Description

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

Examples

 > $\mathrm{with}\left(\mathrm{OrthogonalSeries}\right):$
 > $S≔\mathrm{Create}\left(u\left(n\right),\mathrm{ChebyshevT}\left(n,x\right)\right)$
 ${S}{≔}{\sum }_{{n}{=}{0}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{u}{}\left({n}\right){}{\mathrm{ChebyshevT}}{}\left({n}{,}{x}\right)$ (1)
 > $\mathrm{lprint}\left(S\right)$
 ORTHOGONALSERIES(array(0 .. 1,[(0)=(table(sparse,[("general")=u(n),("bounds")=[0, infinity],("dim")=1,("table")=(table(sparse,[]))])),(1)=(table([("genre")=["ChebyshevT"],("variable")=x,("index")=n]))]))
 > $R≔\mathrm{ConvertToSum}\left(S\right)$
 ${R}{≔}{\sum }_{{n}{=}{0}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{u}{}\left({n}\right){}{\mathrm{ChebyshevT}}{}\left({n}{,}{x}\right)$ (2)
 > $\mathrm{lprint}\left(R\right)$
 Sum(u(n)*ChebyshevT(n,x),n = 0 .. infinity)