Chebyshev lähendamine

Tshebõshevi polünoomid

T[0, x_] := 1;
T[1, x_] := x;
T[n_, x_] := Expand[2 x T[n - 1, x] - T[n - 2, x]]

Tpoly2 = T[2, x]

Tpoly3 = T[3, x]

t1 = Table[ChebyshevT[n, x], {n, 0, 3}]

Plot[Evaluate[t1], {x, -1, 1}];

(2/Pi) 
      NIntegrate[(ArcCos[x])*(-3 x + 4 (x^3))/
            Sqrt[1 - x*x],  {x,  -1,  1}]

Expand[
      3.14159/2  - 
        1.27324*x  -   .141471*(-3 x + 4 (x^3))]

Plot[{ArcCos[x],  
        1.5708 - 0.848827 x - 0.565884 (x^3)},  {x,  -1,  
        1}]