connection with orthogonal polynomials on the line
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11—20 of 400 matching pages
11: Bibliography
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Some orthogonal
-polynomials.
Math. Nachr. 30, pp. 47–61.
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Characterization theorems for orthogonal polynomials.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 1–24.
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Classical Orthogonal Polynomials.
In Orthogonal Polynomials and Applications, C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux (Eds.),
Lecture Notes in Math., Vol. 1171, pp. 36–62.
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Special value of the hypergeometric function and connection formulae among asymptotic expansions.
J. Indian Math. Soc. (N.S.) 51, pp. 161–221.
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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials.
Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
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12: 18.18 Sums
§18.18 Sums
… ►§18.18(ii) Addition Theorems
… ►§18.18(iii) Multiplication Theorems
… ►§18.18(iv) Connection and Inversion Formulas
… ►13: 3.11 Approximation Techniques
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►They enjoy an orthogonal property with respect to integrals:
…as well as an orthogonal property with respect to sums, as follows.
When and , ,
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►For convergence results for Padé approximants, and the connection with continued fractions and Gaussian quadrature, see Baker and Graves-Morris (1996, §4.7).
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14: Bibliography Z
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials.
Proc. London Math. Soc. (3) 65 (1), pp. 1–22.
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“Hidden symmetry” of Askey-Wilson polynomials.
Theoret. and Math. Phys. 89 (2), pp. 1146–1157.
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On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval.
J. Approx. Theory 94 (1), pp. 73–106.
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15: René F. Swarttouw
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►Swarttouw is mainly a teacher of mathematics and has published a few papers on special functions and orthogonal polynomials.
He is coauthor of the book Hypergeometric Orthogonal Polynomials and Their
-Analogues) Hypergeometric Orthogonal Polynomials and Their -Analogues.
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16: 18.36 Miscellaneous Polynomials
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§18.36(ii) Sobolev Orthogonal Polynomials
… ►§18.36(iii) Multiple Orthogonal Polynomials
… ►§18.36(iv) Orthogonal Matrix Polynomials
►These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. … ►§18.36(vi) Exceptional Orthogonal Polynomials
…17: Bibliography K
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Orthogonal Polynomials on -spheres: Gegenbauer, Jacobi and Heun.
In Topics in Polynomials of One and Several Variables and their
Applications,
pp. 299–322.
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Connection formulae for the first Painlevé transcendent in the complex domain.
Lett. Math. Phys. 27 (4), pp. 243–252.
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Connecting Jacobi elliptic functions with different modulus parameters.
Pramana 63 (5), pp. 921–936.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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Lowering and Raising Operators for Some Special Orthogonal Polynomials.
In Jack, Hall-Littlewood and Macdonald Polynomials,
Contemp. Math., Vol. 417, pp. 227–238.
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18: Bibliography B
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Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V.
Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.
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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Ann. of Math. (2) 150 (1), pp. 185–266.
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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The double confluent Heun equation: Characteristic exponent and connection formulae.
Methods Appl. Anal. 1 (3), pp. 348–370.
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19: 18 Orthogonal Polynomials
Chapter 18 Orthogonal Polynomials
…20: Bibliography J
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Bounds on Dawson’s integral occurring in the analysis of a line distribution network for electric vehicles.
Eurandom Preprint Series
Technical Report 14, Eurandom, Eindhoven, The Netherlands.
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Uniform asymptotic expansions for Meixner polynomials.
Constr. Approx. 14 (1), pp. 113–150.
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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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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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The Painlevé connection problem: An asymptotic approach. I.
Stud. Appl. Math. 86 (4), pp. 315–376.
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