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Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Author: Themistocles M. Rassias
Publisher: World Scientific
ISBN: 9789810206147
Category : Mathematics
Languages : en
Pages : 658
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Book Description
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.
Author: Mourad Ismail
Publisher: Cambridge University Press
ISBN: 9780521782012
Category : Mathematics
Languages : en
Pages : 748
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Book Description
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1316061906
Category : Mathematics
Languages : en
Pages : 439
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Book Description
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.
Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
ISBN: 3540310622
Category : Mathematics
Languages : en
Pages : 432
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Book Description
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: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 0521800439
Category : Mathematics
Languages : en
Pages : 408
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Book Description
Orthogonal polynomials of several variables, approximation theory, symmetry-group methods.
Author: Theodore S Chihara
Publisher: Courier Corporation
ISBN: 0486479293
Category : Mathematics
Languages : en
Pages : 276
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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: Gabor Szeg
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 448
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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: I. G. Macdonald
Publisher: Cambridge University Press
ISBN: 9780521824729
Category : Mathematics
Languages : en
Pages : 200
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Book Description
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Author: Paul Nevai
Publisher: Springer Science & Business Media
ISBN: 9400905017
Category : Mathematics
Languages : en
Pages : 472
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Book Description
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.
