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1: 18.30 Associated OP’s

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Numerator and Denominator Polynomials

►The $p_n^{(0)}(x)$ are also referred to as the numerator polynomials, the $p_n(x)$ then being the denominator polynomials, in that the $n$-th approximant of the continued fraction, $z\in ℂ$, … ►

Markov’s Theorem

►The ratio $p_n^{(0)}(z)/p_n(z)$, as defined here, thus provides the same statement of Markov’s Theorem, as in (18.2.9_5), but now in terms of differently obtained numerator and denominator polynomials. …

2: Bibliography I

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More on electrostatic models for zeros of orthogonal polynomials. Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.

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External Links:

ISSN 0163-0563, FullText, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

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3: 18.2 General Orthogonal Polynomials

… ►Because of (18.2.36) the OP’s $p_n(x)$ are also called monic denominator polynomials and the OP’s $p_{n-1}^{(1)}(x)$, or, equivalently, the $p_n^{(0)}(x)$, are called the monic numerator polynomials. …

4: Bibliography G

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A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function. J. Comput. Phys. 42 (2), pp. 277–287.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

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Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.

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External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§3.8(vi).

Encodings:

BibTeX

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On mean convergence of extended Lagrange interpolation. J. Comput. Appl. Math. 43 (1-2), pp. 19–35.

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Notes:

Orthogonal polynomials and numerical methods

External Links:

ISSN 0377-0427, Document, Link, MathReview (Mircea Ivan), ZentralBlatt

Referenced by:

Erratum (V1.0.28) for Table 18.3.1.

Encodings:

BibTeX

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Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation, Oxford University Press, New York.

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Notes:

OPQ, a package of Matlab routines for generating classical and Sobolev orthogonal polynomials, accompanies this book.

External Links:

OPQ, ISBN 0-19-850672-4, MathReview Entry, ZentralBlatt

Referenced by:

(18.2.27), (18.2.28), (18.2.29), (18.2.30), §18.2(ix), §18.40(ii), §18.40(ii), §18.40(i), 3rd item, §3.5(v), Erratum (V1.0.28) for Table 18.3.1.

Encodings:

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Variable-precision recurrence coefficients for nonstandard orthogonal polynomials. Numer. Algorithms 52 (3), pp. 409–418.

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External Links:

ISSN 1017-1398, Document, Link, MathReview Entry

Referenced by:

§18.39(iii), §18.40(ii).

Encodings:

BibTeX

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5: 18.38 Mathematical Applications

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§18.38(i) Classical OP’s: Numerical Analysis

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Differential Equations: Spectral Methods

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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

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6: Bibliography F

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Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London.

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Notes:

Reprinted in 1972 with corrections.

External Links:

MathReview (G. N. Lance), ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

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7: 29.21 Tables

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Arscott and Khabaza (1962) tabulates the coefficients of the polynomials $P$ in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues $h$ for $k^2=0.1(.1)0.9$, $n=1(1)30$. Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.

8: Bibliography S

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Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms. Math. Tables Aids Comput. 9 (52), pp. 164–177.

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External Links:

FullText, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§3.5(viii).

Encodings:

BibTeX

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Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electron. Trans. Numer. Anal. 9, pp. 137–146.

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Notes:

Orthogonal polynomials: numerical and symbolic algorithms (Leganés, 1998)

External Links:

ISSN 1068-9613, FullText, MathReview (Adam Marlewski), ZentralBlatt

Referenced by:

§14.30(i), 3rd item.

Encodings:

BibTeX

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9: Bibliography C

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Stability properties of disk polynomials. Numer. Algorithms.

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External Links:

Document

Referenced by:

(18.14.3_5).

Encodings:

BibTeX

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10: Bibliography L

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Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. Numer. Math. 116 (2), pp. 269–289.

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External Links:

ISSN 0029-599X, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§13.11, §13.11.

Encodings:

BibTeX

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