GetInfo - Maple Help

OrthogonalSeries

 GetInfo
 return information about hypergeometric orthogonal polynomials

 Calling Sequence GetInfo(P, subject, optional_arg)

Parameters

 P - hypergeometric polynomial subject - literal name; one of recurrence, structural, hypergeom, derivative, and derivative_representation optional_arg - (optional) equation of the form root=val where val is an expression

Description

 • The GetInfo(P, subject) command returns information about the hypergeometric polynomial P that depends on the value of subject.
 hypergeom: hypergeometric functional equation satisfied by P and the normalization coefficient of the Rodrigues formula.
 recurrence: three-term recurrence for P.
 derivative: derivative of P.
 structural: structural relation(s). If the optional equation root=val is specified, GetInfo returns the partial structural relation with respect to val. This is available for only continuous hypergeometric polynomials.
 derivative_representation: derivative representation for P. If the optional equation root=val is specified, GetInfo returns the partial derivative representation with respect to val. This is available for only continuous hypergeometric polynomials.

Examples

 > with(OrthogonalSeries) :
 > GetInfo(LaguerreL(n,1,x),derivative_representation);
 ${\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right){=}{\mathrm{LaguerreL}}{}\left({n}{,}{2}{,}{x}\right){-}{\mathrm{LaguerreL}}{}\left({n}{-}{1}{,}{2}{,}{x}\right)$ (1)
 > GetInfo(LaguerreL(n,1,x),hypergeom);
 ${x}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right)\right){+}\left({-}{x}{+}{2}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right)\right){+}{n}{}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right){=}{0}{,}{\mathrm{_B}}{}\left({n}\right){=}\frac{{1}}{{n}{!}}$ (2)
 > GetInfo(LaguerreL(n,1,x),recurrence);
 ${x}{}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right){=}\left({2}{+}{2}{}{n}\right){}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right){+}\left({-}{1}{-}{n}\right){}{\mathrm{LaguerreL}}{}\left({n}{-}{1}{,}{1}{,}{x}\right){+}\left({-}{1}{-}{n}\right){}{\mathrm{LaguerreL}}{}\left({n}{+}{1}{,}{1}{,}{x}\right)$ (3)
 > GetInfo(LaguerreL(n,1,x),structural);
 ${x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right)\right){=}{n}{}{\mathrm{LaguerreL}}{}\left({n}{,}{1}{,}{x}\right){+}\left({-}{1}{-}{n}\right){}{\mathrm{LaguerreL}}{}\left({n}{-}{1}{,}{1}{,}{x}\right)$ (4)
 > GetInfo(JacobiP(n,alpha,beta,x),structural,root=-1);
  (5)
 > GetInfo(HermiteH(n,x),hypergeom);
 $\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right){-}{2}{}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right)\right){+}{2}{}{n}{}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right){=}{0}{,}{\mathrm{_B}}{}\left({n}\right){=}{\left({-1}\right)}^{{n}}$ (6)
 > GetInfo(HermiteH(n,x),structural);
 $\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right){=}{2}{}{n}{}{\mathrm{HermiteH}}{}\left({n}{-}{1}{,}{x}\right)$ (7)
 > GetInfo(HermiteH(n,x),derivative);
 $\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{HermiteH}}{}\left({n}{,}{x}\right){=}{2}{}{n}{}{\mathrm{HermiteH}}{}\left({n}{-}{1}{,}{x}\right)$ (8)
 > GetInfo(ChebyshevT(n,x),structural);
  (9)
 > GetInfo(ChebyshevT(n,x),derivative);
 $\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{ChebyshevT}}{}\left({n}{,}{x}\right){=}{n}{}{\mathrm{ChebyshevU}}{}\left({n}{-}{1}{,}{x}\right)$ (10)