Orthogonal Polynomials And Special Functions Mathematics Essentials

Author : Alma Adams
Publisher : Willford Press
ISBN 13 : 9781647285296
Total Pages : 0 pages
Book Rating : 4.91/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions (Mathematics Essentials) written by Alma Adams and published by Willford Press. This book was released on 2023-09-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal polynomials are a family of polynomials, wherein any two different polynomials in the sequence are orthogonal to each other under some inner product. Classical orthogonal polynomials, Hermite polynomials, Laguerre polynomials, Jacobi polynomials, and Gegenbauer polynomials are a few examples of orthogonal polynomials. These polynomials are used for least square approximations of a function, difference equations, and Fourier series. Another major application of orthogonal polynomials is error-correcting code and sphere packing. Orthogonal polynomials and special functions are useful mathematical functions, which have applications in various fields such as mathematical physics, statistics and probability, and engineering. These can be used to explain many physical and chemical phenomena. This book traces the recent studies in orthogonal polynomials and special functions. A number of latest researches have been included to keep the readers updated with the latest concepts in this area of study. With state-of-the-art inputs by acclaimed experts of mathematics, this book targets students and professionals.

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.24/5 ( download)

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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.

Author : Richard Askey
Publisher : SIAM
ISBN 13 : 9781611970470
Total Pages : 117 pages
Book Rating : 4.74/5 ( download)

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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.

Author : Refaat El Attar
Publisher : Lulu.com
ISBN 13 : 1411666909
Total Pages : 312 pages
Book Rating : 4.00/5 ( download)

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Download or read book Special Functions and Orthogonal Polynomials written by Refaat El Attar and published by Lulu.com. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: (308 Pages). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.

Author : Erik Koelink
Publisher : Springer
ISBN 13 : 3540449450
Total Pages : 259 pages
Book Rating : 4.54/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by Erik Koelink and published by Springer. This book was released on 2003-07-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.

Author : Francisco Marcellan
Publisher :
ISBN 13 : 9786610635061
Total Pages : 418 pages
Book Rating : 4.64/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellan and published by . This book was released on 2006-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Howard S. Cohl
Publisher : Cambridge University Press
ISBN 13 : 1108821596
Total Pages : 351 pages
Book Rating : 4.99/5 ( download)

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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.

Author : Erik Koelink
Publisher :
ISBN 13 : 9783662190548
Total Pages : 260 pages
Book Rating : 4.40/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by Erik Koelink and published by . This book was released on 2014-01-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 249 pages
Book Rating : 4.55/5 ( download)

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Download or read book Orthogonal Polynomials and Special Functions written by and published by . This book was released on 2003 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.16/5 ( download)

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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.