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.

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

$\mathrm{GetInfo}\left(\mathrm{LaguerreL}\left(n\,1\,x\right)\,\mathrm{derivative\_representation}\right)$

$\mathrm{LaguerreL}\left(n\,1\,x\right)=\mathrm{LaguerreL}\left(n\,2\,x\right)-\mathrm{LaguerreL}\left(n-1\,2\,x\right)$

$\mathrm{GetInfo}\left(\mathrm{LaguerreL}\left(n\,1\,x\right)\,\mathrm{hypergeom}\right)$

$x\frac{{\partial }^2}{\partial x^2}\mathrm{LaguerreL}\left(n\,1\,x\right)+\left(-x+2\right)\frac{\partial }{\partial x}\mathrm{LaguerreL}\left(n\,1\,x\right)+n\mathrm{LaguerreL}\left(n\,1\,x\right)=0,\mathrm{\_B}\left(n\right)=\frac{1}{n!}$

$\mathrm{GetInfo}\left(\mathrm{LaguerreL}\left(n\,1\,x\right)\,\mathrm{recurrence}\right)$

$x\mathrm{LaguerreL}\left(n\,1\,x\right)=\left(2+2n\right)\mathrm{LaguerreL}\left(n\,1\,x\right)+\left(-1-n\right)\mathrm{LaguerreL}\left(n-1\,1\,x\right)+\left(-1-n\right)\mathrm{LaguerreL}\left(n+1\,1\,x\right)$

$\mathrm{GetInfo}\left(\mathrm{LaguerreL}\left(n\,1\,x\right)\,\mathrm{structural}\right)$

$x\frac{\partial }{\partial x}\mathrm{LaguerreL}\left(n\,1\,x\right)=n\mathrm{LaguerreL}\left(n\,1\,x\right)+\left(-1-n\right)\mathrm{LaguerreL}\left(n-1\,1\,x\right)$

$\mathrm{GetInfo}\left(\mathrm{JacobiP}\left(n\,\mathrm{\alpha }\,\mathrm{\beta }\,x\right)\,\mathrm{structural}\,\mathrm{root}=-1\right)$

$\left(-x^2+1\right)\frac{\partial }{\partial x}\mathrm{JacobiP}\left(n\,\mathrm{\alpha }\,\mathrm{\beta }\,x\right)=\frac{2\left(\mathrm{\alpha }+\mathrm{\beta }+1+n\right)n\left(\mathrm{\alpha }-\mathrm{\beta }\right)\mathrm{JacobiP}\left(n\,\mathrm{\alpha }\,\mathrm{\beta }\,x\right)}{\left(2n+\mathrm{\alpha }+\mathrm{\beta }+2\right)\left(2n+\mathrm{\alpha }+\mathrm{\beta }\right)}+\frac{2\left(\mathrm{\alpha }+\mathrm{\beta }+1+n\right)\left(n+\mathrm{\beta }\right)\left(n+\mathrm{\alpha }\right)\mathrm{JacobiP}\left(n-1\,\mathrm{\alpha }\,\mathrm{\beta }\,x\right)}{\left(2n+\mathrm{\alpha }+\mathrm{\beta }\right)\left(2n+1+\mathrm{\alpha }+\mathrm{\beta }\right)}-\frac{2\left(\mathrm{\alpha }+\mathrm{\beta }+1+n\right)\left(n+1\right)n\mathrm{JacobiP}\left(n+1\,\mathrm{\alpha }\,\mathrm{\beta }\,x\right)}{\left(2n+\mathrm{\alpha }+\mathrm{\beta }+2\right)\left(2n+1+\mathrm{\alpha }+\mathrm{\beta }\right)}$

$\mathrm{GetInfo}\left(\mathrm{HermiteH}\left(n\,x\right)\,\mathrm{hypergeom}\right)$

$\frac{{\partial }^2}{\partial x^2}\mathrm{HermiteH}\left(n\,x\right)-2x\frac{\partial }{\partial x}\mathrm{HermiteH}\left(n\,x\right)+2n\mathrm{HermiteH}\left(n\,x\right)=0,\mathrm{\_B}\left(n\right)={\left(\mathrm{-1}\right)}^n$

$\mathrm{GetInfo}\left(\mathrm{HermiteH}\left(n\,x\right)\,\mathrm{structural}\right)$

$\frac{\partial }{\partial x}\mathrm{HermiteH}\left(n\,x\right)=2n\mathrm{HermiteH}\left(n-1\,x\right)$

$\mathrm{GetInfo}\left(\mathrm{HermiteH}\left(n\,x\right)\,\mathrm{derivative}\right)$

$\frac{\partial }{\partial x}\mathrm{HermiteH}\left(n\,x\right)=2n\mathrm{HermiteH}\left(n-1\,x\right)$

$\mathrm{GetInfo}\left(\mathrm{ChebyshevT}\left(n\,x\right)\,\mathrm{structural}\right)$

$\left(-x^2+1\right)\frac{\partial }{\partial x}\mathrm{ChebyshevT}\left(n\,x\right)=\frac{n\mathrm{ChebyshevT}\left(n-1\,x\right)}{2}-\frac{n\mathrm{ChebyshevT}\left(n+1\,x\right)}{2}$

$\mathrm{GetInfo}\left(\mathrm{ChebyshevT}\left(n\,x\right)\,\mathrm{derivative}\right)$

$\frac{\partial }{\partial x}\mathrm{ChebyshevT}\left(n\,x\right)=n\mathrm{ChebyshevU}\left(n-1\,x\right)$