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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 monic 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. …
4: Bibliography C
  • B. C. Carlson (2006a) Some reformulated properties of Jacobian elliptic functions. J. Math. Anal. Appl. 323 (1), pp. 522–529.
  • J. M. Carnicer, E. Mainar, and J. M. Peña (2020) Stability properties of disk polynomials. Numer. Algorithms.
  • T. S. Chihara and M. E. H. Ismail (1993) Extremal measures for a system of orthogonal polynomials. Constr. Approx. 9, pp. 111–119.
  • P. A. Clarkson and K. Jordaan (2018) Properties of generalized Freud polynomials. J. Approx. Theory 225, pp. 148–175.
  • J. Crisóstomo, S. Lepe, and J. Saavedra (2004) Quasinormal modes of the extremal BTZ black hole. Classical Quantum Gravity 21 (12), pp. 2801–2809.