# extremal properties

♦
3 matching pages ♦

(0.001 seconds)

## 3 matching pages

##### 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 ${2}^{1-n}{T}_{n}\left(x\right)$, $n\ge 1$, enjoys the “minimax” property on the interval $[-1,1]$, that is, $|{2}^{1-n}{T}_{n}\left(x\right)|$ 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.
…