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extremal properties

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1: 30.15 Signal Analysis
§30.15(v) Extremal Properties
2: Mathematical Introduction
In addition, there is a comprehensive account of the great variety of analytical methods that are used for deriving and applying the extremely important asymptotic properties of the special functions, including double asymptotic properties (Chapter 2 and §§10.41(iv), 10.41(v)). …
3: 18.38 Mathematical Applications
The scaled Chebyshev polynomial 2 1 - n T n ( x ) , n 1 , enjoys the “minimax” property on the interval [ - 1 , 1 ] , that is, | 2 1 - n T n ( x ) | has the least maximum value among all monic polynomials of degree n . In consequence, expansions of functions that are infinitely differentiable on [ - 1 , 1 ] in series of Chebyshev polynomials usually converge extremely rapidly. …