The monomials xj j greaterthanorequalto 0 can be expressed

The monomials {x^j | j greaterthanorequalto 0 can be expressed as combinations of the Chebyshev polynomials. Easily, 1 = T_0(x) and x = T_1(x). Next, x^2 = 1/2 [T_2(x) + 1] = 1/2 T_2(x) + 1/2 T_0(x) Proceeding similarly, express x^3 and x^4 as combinations of Chebyshev polynomials.

T3=4x^3-3x=4x^3-3T1

4x^3=T3+3T1

x^3=(T3+3T1)/4

T4=8x^4-8x^2+1=8x^4-4(T2+T0)+T0

8x^4=T4+4T2+3T0

x^4=(T4+4T2+3T0)/8

$The monomials {x^j | j greaterthanorequalto 0 can be expressed as combinations of the Chebyshev polynomials. Easily, 1 = T_0(x) and x = T_1(x). Next, x^2 = 1/2$

The monomials xj j greaterthanorequalto 0 can be expressed

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