best uniform polynomial approximation
1—10 of 370 matching pages
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials… ►
31.5.2►is a polynomial of degree , and hence a solution of (31.2.1) that is analytic at all three finite singularities . These solutions are the Heun polynomials. …
§35.4 Partitions and Zonal Polynomials… ►
Orthogonal Invariance… ►
Bernoulli Numbers and Polynomials►The origin of the notation , , is not clear. … ►
Euler Numbers and Polynomials… ►The notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
§18.3 Definitions►Table 18.3.1 provides the definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and normalization (§§18.2(i) and 18.2(iii)). … ►For exact values of the coefficients of the Jacobi polynomials , the ultraspherical polynomials , the Chebyshev polynomials and , the Legendre polynomials , the Laguerre polynomials , and the Hermite polynomials , see Abramowitz and Stegun (1964, pp. 793–801). … ►For another version of the discrete orthogonality property of the polynomials see (3.11.9). … ►Legendre polynomials are special cases of Legendre functions, Ferrers functions, and associated Legendre functions (§14.7(i)). …
Uniform asymptotic expansions of a double integral: Coalescence of two stationary points.
Proc. Roy. Soc. London Ser. A 456, pp. 407–431.
Asymptotic expansion of the Krawtchouk polynomials and their zeros.
Comput. Methods Funct. Theory 4 (1), pp. 189–226.
“Best possible” upper and lower bounds for the zeros of the Bessel function
Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.
§3.11(i) Minimax Polynomial Approximations… ►Then there exists a unique th degree polynomial , called the minimax (or best uniform) polynomial approximation to on , that minimizes , where . … ►If we have a sufficiently close approximation … ►
§3.11(iii) Minimax Rational Approximations… ►Then the minimax (or best uniform) rational approximation …
§14.26 Uniform Asymptotic Expansions►The uniform asymptotic approximations given in §14.15 for and for are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). … ►See also Frenzen (1990), Gil et al. (2000), Shivakumar and Wong (1988), Ursell (1984), and Wong (1989) for uniform asymptotic approximations obtained from integral representations.
… ►We are trying to use the best technologies available to make the DLMF content as useful and accessible as we can. … ►Although we have attempted to follow standards and maintain backwards compatibility with older browsers, you will generally get the best results by upgrading to the latest version of your preferred browser.