The discussion revolves around proving that the Chebyshev polynomials, defined as T_n(x) = cos(n arccos(x)), are polynomials of degree n. The original poster questions the validity of this for various values of n, particularly noting discrepancies when n=2 and n=1.
There is an ongoing exploration of the properties of the Chebyshev polynomials, with participants questioning the assumptions made regarding the polynomial nature for different values of n. Some guidance has been suggested regarding the use of induction, but no consensus has been reached on the validity of the polynomial form.
Participants note that the function f(x) = x is a polynomial for n=1, raising questions about the original poster's assertion that it fails for this case. There is also an acknowledgment that the discussion may be overlooking certain aspects of the problem.
Office_Shredder said:It also definitely fails for n=1, but since you started with 2, maybe we're ignoring that