Question

6. Prove that every p E P, has a unique representation of the form: p(x)=a_{0}+a_{1} T_{1}(x)+\cdots+a_{n} T_{n}(x) where T;, for j = 1, ... ,n are the Chebyshev polynomials of

degree j.

Fig: 1

Fig: 2

Fig: 3