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A First Course On Orthogonal Polynomials
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Book Synopsis A First Course on Orthogonal Polynomials by : Kenier Castillo
Download or read book A First Course on Orthogonal Polynomials written by Kenier Castillo and published by CRC Press. This book was released on 2024-11-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials.
Book Synopsis A First Course on Orthogonal Polynomials by : Kenier Castillo
Download or read book A First Course on Orthogonal Polynomials written by Kenier Castillo and published by CRC Press. This book was released on 2024-11-19 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field. Features Suitable for a graduate course in orthogonal polynomials Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials Includes numerous exercises for each topic Real and complex analysis are the only prerequisites
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 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 2014-07-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. 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. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.
Book Synopsis Fourier Series and Orthogonal Polynomials by : Dunham Jackson
Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by American Mathematical Soc.. This book was released on 1941-12-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics. The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence. There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.
Book Synopsis An Introduction to Orthogonal Polynomials by : Theodore Seio Chihara
Download or read book An Introduction to Orthogonal Polynomials written by Theodore Seio Chihara and published by . This book was released on 2014-01-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. 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. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.
Book Synopsis A First Course in Numerical Analysis by : Anthony Ralston
Download or read book A First Course in Numerical Analysis written by Anthony Ralston and published by Courier Corporation. This book was released on 2001-01-01 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
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.
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 1975-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally presented as lectures, the theme of this volume is that one studies orthogonal polynomials and special functions not for their own sake, but to be able to use them to solve problems. The author presents problems suggested by the isometric embedding of projective spaces in other projective spaces, by the desire to construct large classes of univalent functions, by applications to quadrature problems, and theorems on the location of zeros of trigonometric polynomials. There are also applications to combinatorial problems, statistics, and physical problems.
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 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.
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 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 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Book Synopsis A First Course in Numerical Methods by : Uri M. Ascher
Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.
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 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 Orthogonal Polynomials by : Paul Nevai
Download or read book Orthogonal Polynomials written by Paul Nevai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.
