ABSTRACT
We have already established in Section 5.5 that partial sums of first kind expansions
(STn f)(x) = n∑′
ckUk(x), ck = 2 π
f(x)Tk(x)√ 1− x2 dx (7.1)
yield near-minimax approximations within a relative distance of O(log n) in C[−1, 1]. Is this also the case for other kinds of Chebyshev polynomial expansions? The answer is in the affirmative, if we go about the expansion in the right way.
