Chebyshev Polynomials

Concept

started with $T_0=1$ and $T_1=x$

$$T_{k+1}(x)=2x{T}_k(x)-T_{k-1}(x)$$

or

$$T_j(x)=cos(j\cdot arccos(x))$$

therefore it always only defined in $[-1,1]$

Weight

for first-kind Chebyshev Polynomials

$$w(t)=\sqrt{1-t^2}$$