T_0=1
T_1=x
T_2=2x^2-1
...
Anyway, I think Chebyshev Polynomials of the First Kind are done wrong. I want to introduce the polynomial that generates these polynomials.
x^2-2*X*x+1
X±sqrt(X^2-1)
X=cos(θ); sqrt(X^2-1)=i*sin(θ)
2*T_n=(cos(θ)+i*sin(θ))^n+(cos(θ)-i*sin(θ))^n
T_n shares all the properties that Lucas Numbers and Polynomials have. U_n shares all the properties that Fibonacci Numbers and Polynomials have. Well, not exactly. Since it's algebra, the impact is often algebraic. Calculating the sums, for example, is different. Also, I would like to point up that as you go higher in degrees, you gain more Fibonacci/Lucas variants. There are infinite variants in degree two, but they seem to lack meaning. These extra variants that you gain, as you increase the degree, have meaning.
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