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OrthogonalSeries

  

GetInfo

  

return information about hypergeometric orthogonal polynomials

 

Calling Sequence

Parameters

Description

Examples

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

withOrthogonalSeries:

GetInfoLaguerreLn,1,x,derivative_representation

LaguerreLn,1,x=LaguerreLn,2,xLaguerreLn1,2,x

(1)

GetInfoLaguerreLn,1,x,hypergeom

x2x2LaguerreLn,1,x+x+2xLaguerreLn,1,x+nLaguerreLn,1,x=0,_Bn=1n!

(2)

GetInfoLaguerreLn,1,x,recurrence

xLaguerreLn,1,x=2+2nLaguerreLn,1,x+1nLaguerreLn1,1,x+1nLaguerreLn+1,1,x

(3)

GetInfoLaguerreLn,1,x,structural

xxLaguerreLn,1,x=nLaguerreLn,1,x+1nLaguerreLn1,1,x

(4)

GetInfoJacobiPn,α,β,x,structural,root=1

x2+1xJacobiPn,α,β,x=2α+β+1+nnαβJacobiPn,α,β,x2n+α+β+22n+α+β+2α+β+1+nn+βn+αJacobiPn1,α,β,x2n+α+β2n+1+α+β2α+β+1+nn+1nJacobiPn+1,α,β,x2n+α+β+22n+1+α+β

(5)

GetInfoHermiteHn,x,hypergeom

2x2HermiteHn,x2xxHermiteHn,x+2nHermiteHn,x=0,_Bn=1n

(6)

GetInfoHermiteHn,x,structural

xHermiteHn,x=2nHermiteHn1,x

(7)

GetInfoHermiteHn,x,derivative

xHermiteHn,x=2nHermiteHn1,x

(8)

GetInfoChebyshevTn,x,structural

x2+1xChebyshevTn,x=12nChebyshevTn1,x12nChebyshevTn+1,x

(9)

GetInfoChebyshevTn,x,derivative

xChebyshevTn,x=nChebyshevUn1,x

(10)

See Also

ChebyshevT

HermiteH

JacobiP

LaguerreL

OrthogonalSeries

 


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