Szeg? class
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1—10 of 11 matching pages
1: 18.35 Pollaczek Polynomials
2: 18.2 General Orthogonal Polynomials
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The Szegő Class
… ►For OP’s with weight function in the class there are asymptotic formulas as , respectively for outside and for , see Szegő (1975, Theorems 12.1.2, 12.1.4). … ►Generalizations of the Szegő Class
►Nevai (1979, p.39) defined the class of orthogonality measures with support inside such that the absolutely continuous part has in the Szegő class . …3: 18.33 Polynomials Orthogonal on the Unit Circle
4: Bibliography W
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Generating functions of class-numbers.
Compositio Math. 1, pp. 39–68.
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A Treatise on the Theory of Bessel Functions.
2nd edition, Cambridge University Press, Cambridge, England.
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A class of integral transforms.
Proc. Edinburgh Math. Soc. (2) 14, pp. 33–40.
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5: Errata
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►The specific updates to Chapter 18 include some results for general orthogonal polynomials including quadratic transformations, uniqueness of orthogonality measure and completeness, moments, continued fractions, and some special classes of orthogonal polynomials.
…In regard to orthogonal polynomials on the unit circle, we now discuss monic polynomials, Verblunsky’s Theorem, and Szegő’s theorem.
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6: 18.36 Miscellaneous Polynomials
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►Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second order matrix differential equations with coefficients independent of the degree.
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►The possibility of generalization to , for , is implicit in the identity Szegő (1975, page 102),
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7: 18.1 Notation
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Hahn Class OP’s
… ►Wilson Class OP’s
… ►-Hahn Class OP’s
… ►Askey–Wilson Class OP’s
… ►In Szegő (1975, §4.7) the ultraspherical polynomials are denoted by . …8: Bibliography S
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Szegő’s Theorem and Its Descendants. Spectral Theory for Perturbations of Orthogonal Polynomials.
M. B. Porter Lectures, Princeton University Press, Princeton, NJ.
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Szegő polynomials from hypergeometric functions.
Proc. Amer. Math. Soc. 138 (12), pp. 4259–4270.
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Asymptotische Entwicklungen der Jacobischen Polynome.
Schr. der König. Gelehr. Gesell. Naturwiss. Kl. 10, pp. 33–112.
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On certain special sets of orthogonal polynomials.
Proc. Amer. Math. Soc. 1, pp. 731–737.
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Orthogonal Polynomials.
3rd edition, American Mathematical Society, New York.
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9: Bibliography
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Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials.
Comm. Math. Phys. 398 (3), pp. 1291–1348.
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Commentary on the Paper “Beiträge zur Theorie der Toeplitzschen Form”.
In Gábor Szegő, Collected Papers. Vol. 1,
Contemporary Mathematicians, pp. 303–305.
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Singular Continuous Spectrum for a Class of Almost Periodic Jacobi Matrices.
Bulletin of the American Mathematical Society 6 (1), pp. 81–85.
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10: Bibliography E
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The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature.
J. Comput. Appl. Math. 61 (1), pp. 43–72.
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Generating functions of certain continuous orthogonal systems.
Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.
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On Lamé functions.
Philos. Mag. (7) 31, pp. 123–130.
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On algebraic Lamé functions.
Philos. Mag. (7) 32, pp. 348–350.
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Generalized Bernoulli numbers, generalized irregular primes, and class number.
Ann. Univ. Turku. Ser. A I 178, pp. 1–72.
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