orthogonal matrix polynomials

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21: Bibliography R

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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

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ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

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The Associated Classical Orthogonal Polynomials. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 255–279.

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External Links:

MathReview (Wadim Zudilin), ZentralBlatt

Referenced by:

§18.30(viii).

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.

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ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt

Referenced by:

§35.9.

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22: 3.11 Approximation Techniques

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§3.11(i) Minimax Polynomial Approximations

… ►They enjoy an orthogonal property with respect to integrals: …When $n>0$ and $0\le j\le n$, $0\le k\le n$, … ►The matrix is symmetric and positive definite, but the system is ill-conditioned when $n$ is large because the lower rows of the matrix are approximately proportional to one another. … ► …

23: Bibliography F

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II. J. Math. Anal. Appl. 7 (3), pp. 440–451.

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Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.11(iii).

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. J. Math. Anal. Appl. 6 (3), pp. 394–403.

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Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.11(iii).

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III. J. Math. Anal. Appl. 12 (3), pp. 593–601.

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Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§16.11(iii).

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On the coefficients in the recursion formulae of orthogonal polynomials. Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.

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MathReview (A. G. Law), ZentralBlatt

Referenced by:

§18.32, §32.15.

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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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24: Bibliography C

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Work Group of Computational Mathematics, University of Kassel, Germany.

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Notes:

Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

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CAOP

Referenced by:

1st item.

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Asymptotics of the largest zeros of some orthogonal polynomials. J. Phys. A 31 (25), pp. 5525–5544.

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ISSN 0305-4470, Document, MathReview (Tim H. Baker), ZentralBlatt

Referenced by:

§18.26(v), §18.29.

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An Introduction to Orthogonal Polynomials. Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.

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ISBN 0-677-04150-0, MathReview (A. G. Law), ZentralBlatt

Referenced by:

§1.16(ix), (18.2.33), (18.2.36), (18.2.38), §18.2(v), §18.2(iii), §18.2(iv), §18.2(vii), §18.2(x), §18.20(i), (18.30.25), §18.30(ii), §18.30, §18.40(ii), Ch.18.

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Extremal measures for a system of orthogonal polynomials. Constr. Approx. 9, pp. 111–119.

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ISSN 0176-4276, Document, MathReview (Mizan Rahman), ZentralBlatt

Referenced by:

§18.28(iv).

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Basic hypergeometric functions and orthogonal Laurent polynomials. Proc. Amer. Math. Soc. 140 (6), pp. 2075–2089.

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ISSN 0002-9939, Link, MathReview (Roelof Koekoek), ZentralBlatt

Referenced by:

§18.33(iv).

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25: 35.5 Bessel Functions of Matrix Argument

§35.5 Bessel Functions of Matrix Argument

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§35.5(i) Definitions

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§35.5(ii) Properties

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§35.5(iii) Asymptotic Approximations

►For asymptotic approximations for Bessel functions of matrix argument, see Herz (1955) and Butler and Wood (2003).

26: Bibliography J

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Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.

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External Links:

FullText, MathReview (I. Olkin), ZentralBlatt

Referenced by:

§35.11, §35.4(i), §35.4(ii), §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35.

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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.

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ISSN 0167-2789, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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Uniform asymptotic expansions for Meixner polynomials. Constr. Approx. 14 (1), pp. 113–150.

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ISSN 0176-4276, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§18.24, §2.4(vi).

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Asymptotic formulas for the zeros of the Meixner polynomials. J. Approx. Theory 96 (2), pp. 281–300.

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ISSN 0021-9045, Document, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§18.24.

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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function. In Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.

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External Links:

MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§5.10, §5.10.

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

Referenced by:

§3.5(viii).

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Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.

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External Links:

ISBN 0-8218-3446-0, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

(18.33.17), (18.33.18), (18.33.21), (18.33.22), (18.33.23), (18.33.24), (18.33.25), (18.33.26), (18.33.27), (18.33.28), (18.33.30), (18.33.31), (18.33.32), §18.33(vi), §18.33(i), §18.33(vi).

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Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.

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External Links:

ISBN 0-8218-3675-7, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

§18.33(i), §18.33(vi).

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On certain special sets of orthogonal polynomials. Proc. Amer. Math. Soc. 1, pp. 731–737.

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ISSN 0002-9939, Document, Link, MathReview (A. C. Offord)

Referenced by:

§18.35(i).

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Orthogonal Polynomials. 3rd edition, American Mathematical Society, New York.

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Notes:

American Mathematical Society Colloquium Publications, Vol. 23

External Links:

MathReview (J. Burlak)

Referenced by:

Ch.14, §9.1, Notations A.

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28: Bibliography W

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Global asymptotics of the Meixner polynomials. Asymptotic Analysis 75 (3-4), pp. 211–231.

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ISSN 0921-7134, Document, MathReview (Mario Pérez Riera), ZentralBlatt

Referenced by:

§18.24, §18.24.

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Asymptotics of orthogonal polynomials via recurrence relations. Anal. Appl. (Singap.) 10 (2), pp. 215–235.

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ISSN 0219-5305, Document, Link, MathReview (Li Zhong Peng), ZentralBlatt

Referenced by:

§2.9(iii), §2.9(iii).

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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules. Ann. Inst. Statist. Math. 45 (3), pp. 467–475.

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ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt

Referenced by:

§35.9.

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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials. Ph.D. Thesis, University of Wisconsin, Madison, WI.

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Referenced by:

§16.4(iii), §16.4(iii), §16.4(iii).

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Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11 (4), pp. 690–701.

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ISSN 0036-1410, Document, MathReview (R. G. Buschman), ZentralBlatt

Referenced by:

§18.25(i), §18.25(i), §18.25(ii), §18.25(iii), §18.26(i), §18.26(ii), §18.38(iii).

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