The Chebyshev polynomials: (a) Prove that Tn(t) = cos(n arccos t), n = 0, 1, 2,... form
Question:
(a) Prove that
Tn(t) = cos(n arccos t), n = 0, 1, 2,...
form a system of orthogonal polynomials under the weighted inner product
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(b) What is || Tn ||?
(c) Write out the formulae for T0(t),.... T6(t) and plot their graphs.
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a To prove orthogonality use the change of variables t cos in the inner prod...View the full answer
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