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Author: Mourad Ismail
Publisher: Cambridge University Press
Published: 2005-11-21
Total Pages: 748
ISBN-13: 9780521782012
DOWNLOAD EBOOK →The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Author: Mourad E. H. Ismail
Publisher:
Published: 2005
Total Pages: 728
ISBN-13: 9781139882811
DOWNLOAD EBOOK →The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Author: Arnold F. Nikiforov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 388
ISBN-13: 3642747485
DOWNLOAD EBOOK →While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
Author: Doman Brian George Spencer
Publisher: World Scientific
Published: 2015-09-18
Total Pages: 176
ISBN-13: 9814704059
DOWNLOAD EBOOK →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.
Author: Mama Foupouagnigni
Publisher: Springer Nature
Published: 2020-03-11
Total Pages: 683
ISBN-13: 3030367444
DOWNLOAD EBOOK →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.
Author: Gabor Szeg
Publisher: American Mathematical Soc.
Published: 1939-12-31
Total Pages: 448
ISBN-13: 0821810235
DOWNLOAD EBOOK →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.
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
Published: 2006-06-19
Total Pages: 432
ISBN-13: 3540310622
DOWNLOAD EBOOK →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.
Author: Francisco Marcellán
Publisher: Springer Nature
Published: 2021
Total Pages: 327
ISBN-13: 3030561909
DOWNLOAD EBOOK →The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.
Author: Jorge Arves
Publisher: American Mathematical Soc.
Published: 2012-09-11
Total Pages: 266
ISBN-13: 0821868969
DOWNLOAD EBOOK →This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.
Author: Saber Elaydi
Publisher: World Scientific
Published: 2007
Total Pages: 789
ISBN-13: 9812706437
DOWNLOAD EBOOK →This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
