Chebyshev Polynomials

Manipulate[Plot[Evaluate[If[!a||(n>15&&ControlActive[]),
ChebyshevT[n,x],Array[ChebyshevT[#,x]&,n+1,0]]],{x,-1,1},
PlotRange->{-1,1},ImageSize->{500,400},PlotLabel->Style[With[{n=n},y==HoldForm[ChebyshevT[n,x]]],14]],
{{n,3,"order"},0,35,1},
{{a,False,"show lower orders"},{True,False}},TrackedSymbols:>{n,a}]

CAPTION

The Chebyshev polynomials are orthogonal polynomials used in many disparate areas of pure and applied mathematics.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Chebyshev Polynomials" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ChebyshevPolynomials/

Contributed by: Stephen Wolfram

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