Orthogonal Polynomials

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821810235
Total Pages : 432 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials by : Gabor Szegš

Download or read book Orthogonal Polynomials written by Gabor Szegš and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.

An Introduction to Orthogonal Polynomials

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Publisher : Courier Corporation
ISBN 13 : 0486479293
Total Pages : 276 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis An Introduction to Orthogonal Polynomials by : Theodore S Chihara

Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2011-02-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--

Classical and Quantum Orthogonal Polynomials in One Variable

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521782012
Total Pages : 748 pages
Book Rating : 4.7/5 (82 download)

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Book Synopsis Classical and Quantum Orthogonal Polynomials in One Variable by : Mourad Ismail

Download or read book Classical and Quantum Orthogonal Polynomials in One Variable written by Mourad Ismail and published by Cambridge University Press. This book was released on 2005-11-21 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

Hypergeometric Orthogonal Polynomials and Their q-Analogues

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 364205014X
Total Pages : 578 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Hypergeometric Orthogonal Polynomials and Their q-Analogues by : Roelof Koekoek

Download or read book Hypergeometric Orthogonal Polynomials and Their q-Analogues written by Roelof Koekoek and published by Springer Science & Business Media. This book was released on 2010-03-18 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821826956
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach by : Percy Deift

Download or read book Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach written by Percy Deift and published by American Mathematical Soc.. This book was released on 2000 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

The Classical Orthogonal Polynomials

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Publisher : World Scientific
ISBN 13 : 9814704059
Total Pages : 176 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis The Classical Orthogonal Polynomials by : Doman Brian George Spencer

Download or read book The Classical Orthogonal Polynomials written by Doman Brian George Spencer and published by World Scientific. This book was released on 2015-09-18 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.

Orthogonal Polynomials on the Unit Circle

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821848631
Total Pages : 466 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials on the Unit Circle by : Barry Simon

Download or read book Orthogonal Polynomials on the Unit Circle written by Barry Simon and published by American Mathematical Soc.. This book was released on 2009-08-05 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.

Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 082180359X
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials by : Alouf Jirari

Download or read book Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials written by Alouf Jirari and published by American Mathematical Soc.. This book was released on 1995 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-written book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate $L^2$ setting, the book gives necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still self-adjoint when restricted to ``energy norms''. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.

Stochastic Processes and Orthogonal Polynomials

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Publisher : Springer Science & Business Media
ISBN 13 : 1461211700
Total Pages : 170 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Processes and Orthogonal Polynomials by : Wim Schoutens

Download or read book Stochastic Processes and Orthogonal Polynomials written by Wim Schoutens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and diffusions, martingale relations for Lévy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis. Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium.

Orthogonal Polynomials

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Author :
Publisher : Pergamon
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Orthogonal Polynomials by : Géza Freud

Download or read book Orthogonal Polynomials written by Géza Freud and published by Pergamon. This book was released on 1971 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals.

Orthogonal Polynomials

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Author :
Publisher : OUP Oxford
ISBN 13 : 0191545058
Total Pages : 312 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Orthogonal Polynomials by : Walter Gautschi

Download or read book Orthogonal Polynomials written by Walter Gautschi and published by OUP Oxford. This book was released on 2004-04-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

Orthogonal Polynomials

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Author :
Publisher : de Gruyter
ISBN 13 : 9783110313857
Total Pages : 510 pages
Book Rating : 4.3/5 (138 download)

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Book Synopsis Orthogonal Polynomials by : Evguenii A. Rakhmanov

Download or read book Orthogonal Polynomials written by Evguenii A. Rakhmanov and published by de Gruyter. This book was released on 2020-05-07 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the theory of orthogonal polynomials go back at least to the 18th century when they were studied in terms of continued fractions. The theory is now large and complex: a crossroad of several important domains of analysis such as analytic function theory, analytic theory of differential equations, Fourier and harmonic analysis, spectral theory of Sturm-Liouville operators, and approximation and interpolation, among others.

Orthogonal Polynomials

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Author :
Publisher : Springer Nature
ISBN 13 : 3030367444
Total Pages : 683 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni

Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.

From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

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Publisher : Springer Nature
ISBN 13 : 3030754251
Total Pages : 388 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory by : Fritz Gesztesy

Download or read book From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory written by Fritz Gesztesy and published by Springer Nature. This book was released on 2021-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

Orthogonal Polynomials and Special Functions

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Author :
Publisher : SIAM
ISBN 13 : 0898710189
Total Pages : 115 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Richard Askey

Download or read book Orthogonal Polynomials and Special Functions written by Richard Askey and published by SIAM. This book was released on 1975-06-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.

Orthogonal Polynomials and Special Functions

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Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Francisco Marcellàn

Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellàn and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

Discrete Orthogonal Polynomials. (AM-164)

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Author :
Publisher : Princeton University Press
ISBN 13 : 0691127344
Total Pages : 178 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Discrete Orthogonal Polynomials. (AM-164) by : J. Baik

Download or read book Discrete Orthogonal Polynomials. (AM-164) written by J. Baik and published by Princeton University Press. This book was released on 2007 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description