Gaussian polynomials

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21: Bibliography S

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A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals. Comput. Phys. Comm. 66 (2-3), pp. 271–275.

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External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

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Gaussian-transform method for molecular integrals. I. Formulation for energy integrals. J. Chem. Phys. 43 (2), pp. 398–414.

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External Links:

Document, MathReview (R. K. Nesbet)

Referenced by:

§8.24(i).

Encodings:

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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.

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Referenced by:

§8.24(i), §8.24(iii).

Encodings:

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Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.

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External Links:

ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§18.2(xii).

Encodings:

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Gaussian Quadrature Formulas. Prentice-Hall Inc., Englewood Cliffs, N.J..

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External Links:

MathReview (P. C. Hammer), ZentralBlatt

Referenced by:

§3.5(v).

Encodings:

BibTeX

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22: Bibliography C

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A note on Euler numbers and polynomials. Nagoya Math. J. 7, pp. 35–43.

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External Links:

MathReview (A. L. Whiteman), ZentralBlatt

Referenced by:

§24.10(iv).

Encodings:

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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:

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Numerical evaluation of the Lambert $W$ function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Trans. Signal Process. 50 (9), pp. 2160–2165.

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External Links:

ISSN 1053-587X, Document, MathReview (J. Borwein), ZentralBlatt

Referenced by:

§4.44, §4.45(iii).

Encodings:

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Properties of generalized Freud polynomials. J. Approx. Theory 225, pp. 148–175.

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External Links:

ISSN 0021-9045, Document, Link, MathReview (Maria das Neves Rebocho)

Referenced by:

§18.32.

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The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§32.8(iv).

Encodings:

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23: 3.11 Approximation Techniques

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§3.11(i) Minimax Polynomial Approximations

… ► … ►For convergence results for Padé approximants, and the connection with continued fractions and Gaussian quadrature, see Baker and Graves-Morris (1996, §4.7). … ►Suppose a function $f(x)$ is approximated by the polynomial … ►Splines are defined piecewise and usually by low-degree polynomials. …

24: Errata

… ►We have significantly expanded the section on associated orthogonal polynomials, including expanded properties of associated Laguerre, Hermite, Meixner–Pollaczek, and corecursive orthogonal and numerator and denominator orthogonal polynomials. …In regard to orthogonal polynomials on the unit circle, we now discuss monic polynomials, Verblunsky’s Theorem, and Szegő’s theorem. We also discuss non-classical Laguerre polynomials and give much more details and examples on exceptional orthogonal polynomials. We have also completely expanded our discussion on applications of orthogonal polynomials in the physical sciences, and also methods of computation for orthogonal polynomials. … ►

Originally the matrix in the argument of the Gaussian hypergeometric function of matrix argument ${}_2{}^{}F_1^{}$ was written with round brackets. This matrix has been rewritten with square brackets to be consistent with the rest of the DLMF.

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25: 3.2 Linear Algebra

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§3.2(i) Gaussian Elimination

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Iterative Refinement

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§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix

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