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Author: Gabor Szeg Publisher: American Mathematical Soc. ISBN: 0821810235 Category : Mathematics Languages : en Pages : 432
Book Description
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: Gabor Szeg Publisher: American Mathematical Soc. ISBN: 0821810235 Category : Mathematics Languages : en Pages : 432
Book Description
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: Theodore S Chihara Publisher: Courier Corporation ISBN: 0486479293 Category : Mathematics Languages : en Pages : 276
Book Description
"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"--
Author: Dunham Jackson Publisher: Courier Corporation ISBN: 9780486438085 Category : Mathematics Languages : en Pages : 260
Book Description
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, more. 1941 edition.
Author: P. K. Suetin Publisher: CRC Press ISBN: 9789056991678 Category : Mathematics Languages : en Pages : 494
Book Description
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.
Author: Walter Gautschi Publisher: Birkhäuser ISBN: 3034886853 Category : Technology & Engineering Languages : en Pages : 275
Book Description
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.
Author: Renato Alvarez-Nodarse Publisher: Nova Publishers ISBN: 9781594540097 Category : Mathematics Languages : en Pages : 222
Book Description
This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.
Author: Mama Foupouagnigni Publisher: Springer Nature ISBN: 3030367444 Category : Mathematics Languages : en Pages : 683
Book Description
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: Walter Gautschi Publisher: OUP Oxford ISBN: 0191545058 Category : Mathematics Languages : en Pages : 312
Book Description
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.
Author: Walter Gautschi Publisher: SIAM ISBN: 1611974291 Category : Science Languages : en Pages : 345
Book Description
Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years. Orthogonal Polynomials in MATLAB: Exercises and Solutions describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.
Author: Gabor Szeg
Author: Gabor Szeg
Author: Theodore S Chihara
Author: Dunham Jackson
Author: P. K. Suetin
Author: Walter Gautschi
Author: Mourad Ismail
Author: Renato Alvarez-Nodarse
Author: Mama Foupouagnigni
Author: Walter Gautschi
Author: Walter Gautschi