Mathematica cells for Chebyshev polynomials of the second kind

 

(* Atlas for Computing Mathematical Functions

    by William J. Thompson *)

 

(* You MUST execute this cell first *)

(*  Numerical Tables of Orthogonal Polynomials 

    depending on just n and x *)

NumTableOP[poly_,name_,maxn_,xmin_,xmax_,xstep_] :=

    N[TableForm[Table[{n,poly[n,x]},

      {x,xmin,xmax,xstep},{n,0,maxn}],

      TableHeadings-> {None,{"n",""<>ToString[name]<>"(x)"}}],10]

 

(* ChebyU cell *)

(*   Chebyshev Polynomials of Second Kind, Un *)    

ChebySecondChart = Plot3D[

    ChebyshevU[n,x],{x,-0.9,0.9},{n,2,8},

     PlotRange->All,PlotPoints->{30,30},

     Ticks->{Automatic,Automatic,None},

     PlotLabel->"Chebyshev Un(x)",

      AxesEdge->{Automatic,{1,-1},Automatic},

      AxesLabel->{"x"," n"," "}];

(*  Chebyshev Un: Numerical *)

NumTableOP[ChebyshevU,Un,4,-1,1,0.5]