Download or read book Classical Orthogonal Polynomials of a Discrete Variable written by Arnold F. Nikiforov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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.
Download or read book Orthogonal Polynomials of Several Variables written by Charles F. Dunkl and published by Cambridge University Press. This book was released on 2014-08-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It covers the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains. The approach is a blend of classical analysis and symmetry group theoretic methods. Finite reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. This revised edition has been updated throughout to reflect recent developments in the field. It contains 25% new material, including two brand new chapters on orthogonal polynomials in two variables, which will be especially useful for applications, and orthogonal polynomials on the unit sphere. The most modern and complete treatment of the subject available, it will be useful to a wide audience of mathematicians and applied scientists, including physicists, chemists and engineers.
Download or read book Orthogonal Polynomials in Two Variables written by P. K. Suetin and published by CRC Press. This book was released on 1999-08-19 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
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.
Download or read book Encyclopedia of Special Functions The Askey Bateman Project written by Mourad E. H. Ismail and published by Cambridge University Press. This book was released on 2020-09-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive update of the Bateman Manuscript Project. Volume 1 covers orthogonal polynomials and moment problems.
Download or read book Orthogonal Polynomials of Several Variables written by Charles F. Dunkl and published by Cambridge University Press. This book was released on 2014-08-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
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"--
Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 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.
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.
Download or read book Difference Equations and Discrete Dynamical Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthogonal Polynomials Current Trends and Applications written by Francisco Marcellán and published by Springer Nature. This book was released on 2021 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Orthogonal Polynomials in the Spectral Analysis of Markov Processes written by Manuel Domínguez de la Iglesia and published by Cambridge University Press. This book was released on 2021-10-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.
Download or read book Discrete Orthogonal Polynomials AM 164 written by J. Baik and published by Princeton University Press. This book was released on 2007-01-02 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Download or read book Topics in Polynomials of One and Several Variables and Their Applications written by Themistocles M. Rassias and published by World Scientific. This book was released on 1993 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
Download or read book Classical and Quantum Orthogonal Polynomials in One Variable written by Mourad E. H. Ismail and published by . This book was released on 2005 with total page 728 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.
