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General Orthogonal Polynomials
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Book Synopsis General Orthogonal Polynomials by : Herbert Stahl
Download or read book General Orthogonal Polynomials written by Herbert Stahl and published by Cambridge University Press. This book was released on 1992-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Book Synopsis Orthogonal Polynomials by : Gabor Szeg
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.
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"--
Book Synopsis Discrete Orthogonal Polynomials. (AM-164) by : Jinho Baik
Download or read book Discrete Orthogonal Polynomials. (AM-164) written by Jinho 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
Book Synopsis Orthogonal Polynomials of Several Variables by : Charles F. Dunkl
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.
Book Synopsis The Classical Orthogonal Polynomials by : Brian George Spencer Doman
Download or read book The Classical Orthogonal Polynomials written by Brian George Spencer Doman and published by World Scientific. This book was released on 2015-09-18 with total page 177 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.
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.
Book Synopsis Fourier Series In Orthogonal Polynomials by : Boris Osilenker
Download or read book Fourier Series In Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999-04-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness).The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L2μ; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5).The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials.The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones.Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment.This book is intended for researchers (mathematicians, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.
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.
Book Synopsis Polynomes Orthogonaux et Applications by : C. Brezinski
Download or read book Polynomes Orthogonaux et Applications written by C. Brezinski and published by Springer. This book was released on 2006-11-22 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical Orthogonal Polynomials of a Discrete Variable by : Arnold F. Nikiforov
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.
Book Synopsis Special Functions in Physics with MATLAB by : Wolfgang Schweizer
Download or read book Special Functions in Physics with MATLAB written by Wolfgang Schweizer and published by Springer Nature. This book was released on 2021-03-25 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.
Book Synopsis Topics in Polynomials of One and Several Variables and Their Applications by : Themistocles M. Rassias
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.
Book Synopsis Frontiers In Orthogonal Polynomials And Q-series by : M Zuhair Nashed
Download or read book Frontiers In Orthogonal Polynomials And Q-series written by M Zuhair Nashed and published by World Scientific. This book was released on 2018-01-12 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Book Synopsis Orthogonal Polynomials and Painlevé Equations by : Walter Van Assche
Download or read book Orthogonal Polynomials and Painlevé Equations written by Walter Van Assche and published by Cambridge University Press. This book was released on 2018 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.
Book Synopsis Orthogonal Polynomials for Exponential Weights by : A. L. Levin
Download or read book Orthogonal Polynomials for Exponential Weights written by A. L. Levin and published by Springer Science & Business Media. This book was released on 2001-06-29 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0 ; likewise, the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov-Bernstein and Nikolskii inequalities. The book will be of interest to researchers in approximation theory, harmonic analysis, numerical analysis, potential theory, and all those that apply orthogonal polynomials.
Book Synopsis Lectures on Orthogonal Polynomials and Special Functions by : Howard S. Cohl
Download or read book Lectures on Orthogonal Polynomials and Special Functions written by Howard S. Cohl and published by Cambridge University Press. This book was released on 2020-10-15 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
