OrthogonalSeries - Maple Programming Help

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OrthogonalSeries

 Degree
 return the degree of a series with respect to one or more variables

 Calling Sequence Degree(S, x) Degree(S, [x1,.., xn]) Degree(S)

Parameters

 S - orthogonal series x, x1, .., xn - names

Description

 • If S is a finite series, then the Degree(S, x) calling sequence returns the degree of S with respect to the variable x. If S is an infinite series, then the result is infinity.
 • The Degree(S, [x1,.., xn]) calling sequence returns [Degree(S, x1),..., Degree(S, xn)].
 • The Degree(S) calling sequence returns the maximum degree of S with respect to its variables. This allows the user to test whether a series is finite.

Examples

 > $\mathrm{with}\left(\mathrm{OrthogonalSeries}\right):$
 > $S≔\mathrm{Create}\left(\left[\left(0,0\right)=3,\left(1,2\right)=-1,\left(3,2\right)=\mathrm{α}\right],\mathrm{GegenbauerC}\left(n,1,x\right),\mathrm{LaguerreL}\left(m,1,y\right)\right)$
 ${S}{≔}{3}{}{\mathrm{GegenbauerC}}{}\left({0}{,}{1}{,}{x}\right){}{\mathrm{LaguerreL}}{}\left({0}{,}{1}{,}{y}\right){-}{\mathrm{GegenbauerC}}{}\left({1}{,}{1}{,}{x}\right){}{\mathrm{LaguerreL}}{}\left({2}{,}{1}{,}{y}\right){+}{\mathrm{α}}{}{\mathrm{GegenbauerC}}{}\left({3}{,}{1}{,}{x}\right){}{\mathrm{LaguerreL}}{}\left({2}{,}{1}{,}{y}\right)$ (1)
 > $\mathrm{Degree}\left(S,x\right);$$\mathrm{Degree}\left(S,y\right);$$\mathrm{Degree}\left(S,\left[x,y\right]\right)$
 ${3}$
 ${2}$
 $\left[{3}{,}{2}\right]$ (2)
 > $\mathrm{Degree}\left(S\right)$
 ${3}$ (3)
 > $\mathrm{S1}≔\mathrm{Create}\left(\left\{\frac{1}{{n}^{2}},n=1..\mathrm{∞}\right\},\mathrm{ChebyshevT}\left(n,x\right)\right)$
 ${\mathrm{S1}}{≔}{\sum }_{{n}{=}{1}}^{{\mathrm{∞}}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\frac{{\mathrm{ChebyshevT}}{}\left({n}{,}{x}\right)}{{{n}}^{{2}}}$ (4)
 > $\mathrm{Degree}\left(\mathrm{S1},x\right);$$\mathrm{Degree}\left(\mathrm{S1},y\right);$$\mathrm{Degree}\left(\mathrm{S1}\right)$
 ${\mathrm{∞}}$
 ${0}$
 ${\mathrm{∞}}$ (5)
 > $\mathrm{S2}≔\mathrm{Create}\left(\left\{\left[0=1,N=2\right],\frac{1}{{n}^{2}},n=3..8\right\},\mathrm{ChebyshevT}\left(n,x\right)\right)$
 ${\mathrm{S2}}{≔}{\mathrm{ChebyshevT}}{}\left({0}{,}{x}\right){+}{2}{}{\mathrm{ChebyshevT}}{}\left({N}{,}{x}\right){+}{\sum }_{{n}{=}{3}}^{{8}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\frac{{\mathrm{ChebyshevT}}{}\left({n}{,}{x}\right)}{{{n}}^{{2}}}$ (6)
 > $\mathrm{Degree}\left(\mathrm{S2}\right)$
 ${\mathrm{max}}{}\left({8}{,}{N}\right)$ (7)