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203w07hw6 - Prove that T n def = cos n arccos x is a...

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EECS 203, Discrete Mathematics Winter 2007, University of Michigan, Ann Arbor Problem Set 6 Problems from the Textbook 4.1: 40[E], 48[E], 50[C] 4.2: 4[E], 26[E], 34[M] 4.3: 18[M], 24[E], 44[M], 46[E] * Extra Credit Problem A6.1 ( Extra Credit).
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Unformatted text preview: Prove that T n def = cos( n arccos( x )) is a polynomial of degree n for x ∈ [-1 , 1]. This polynomial is called the Chebyshev polynomial of the first kind, a polynomial having several extremal properties. 1...
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