Recent Advances In Orthogonal Polynomials Special Functions And Their Applications

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Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications

Author : Jorge Arves
Publisher : American Mathematical Soc.
ISBN 13 : 0821868969
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications by : Jorge Arves

Download or read book Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications written by Jorge Arves and published by American Mathematical Soc.. This book was released on 2012-09-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.

Orthogonal Polynomials and Special Functions

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.5/5 (43 download)

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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.

Orthogonal Polynomials and Special Functions

Author : Richard Askey
Publisher : SIAM
ISBN 13 : 9781611970470
Total Pages : 117 pages
Book Rating : 4.9/5 (74 download)

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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.

Laredo Lectures on Orthogonal Polynomials and Special Functions

Author : Renato Alvarez-Nodarse
Publisher : Nova Publishers
ISBN 13 : 9781594540097
Total Pages : 222 pages
Book Rating : 4.5/5 (4 download)

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Book Synopsis Laredo Lectures on Orthogonal Polynomials and Special Functions by : Renato Alvarez-Nodarse

Download or read book Laredo Lectures on Orthogonal Polynomials and Special Functions written by Renato Alvarez-Nodarse and published by Nova Publishers. This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Special Functions and Orthogonal Polynomials

Author : AMS Special Session on Special Functions and Orthogonal Polynomials
Publisher : American Mathematical Soc.
ISBN 13 : 0821846507
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Special Functions and Orthogonal Polynomials by : AMS Special Session on Special Functions and Orthogonal Polynomials

Download or read book Special Functions and Orthogonal Polynomials written by AMS Special Session on Special Functions and Orthogonal Polynomials and published by American Mathematical Soc.. This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.

Theory and Application of Special Functions

Author : Richard Askey
Publisher : Academic Press
ISBN 13 : 1483216160
Total Pages : 573 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Theory and Application of Special Functions by : Richard Askey

Download or read book Theory and Application of Special Functions written by Richard Askey and published by Academic Press. This book was released on 2014-05-10 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.4/5 (9 download)

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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.

Lectures on Orthogonal Polynomials and Special Functions

Author : Howard S. Cohl
Publisher : Cambridge University Press
ISBN 13 : 1108905420
Total Pages : 352 pages
Book Rating : 4.1/5 (89 download)

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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.

Special Functions 2000: Current Perspective and Future Directions

Author : Joaquin Bustoz
Publisher : Springer Science & Business Media
ISBN 13 : 9401008183
Total Pages : 521 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Special Functions 2000: Current Perspective and Future Directions by : Joaquin Bustoz

Download or read book Special Functions 2000: Current Perspective and Future Directions written by Joaquin Bustoz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.

Special Functions

Author : George E. Andrews
Publisher : Cambridge University Press
ISBN 13 : 9780521789882
Total Pages : 684 pages
Book Rating : 4.7/5 (898 download)

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Book Synopsis Special Functions by : George E. Andrews

Download or read book Special Functions written by George E. Andrews and published by Cambridge University Press. This book was released on 1999 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Special Functions and Orthogonal Polynomials

Author : Refaat El Attar
Publisher : Lulu.com
ISBN 13 : 1411666909
Total Pages : 312 pages
Book Rating : 4.4/5 (116 download)

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Book Synopsis Special Functions and Orthogonal Polynomials by : Refaat El Attar

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.

An Introduction to Orthogonal Polynomials

Author : Theodore S Chihara
Publisher : Courier Corporation
ISBN 13 : 0486479293
Total Pages : 276 pages
Book Rating : 4.4/5 (864 download)

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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"--

Special Functions & Their Applications

Author : N. N. Lebedev
Publisher : Courier Corporation
ISBN 13 : 0486139891
Total Pages : 340 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Special Functions & Their Applications by : N. N. Lebedev

Download or read book Special Functions & Their Applications written by N. N. Lebedev and published by Courier Corporation. This book was released on 2012-04-30 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

Orthogonal Polynomials and Special Functions

Author : Francisco Marcellan
Publisher :
ISBN 13 : 9786610635061
Total Pages : 418 pages
Book Rating : 4.6/5 (35 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Francisco Marcellan

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:

Recent Advances in Scientific Computing and Applications

Author : Jichun Li
Publisher : American Mathematical Soc.
ISBN 13 : 0821887378
Total Pages : 397 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Scientific Computing and Applications by : Jichun Li

Download or read book Recent Advances in Scientific Computing and Applications written by Jichun Li and published by American Mathematical Soc.. This book was released on 2013-04-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.

Recent Advances in Real Complexity and Computation

Author : Luis M. Pardo
Publisher : American Mathematical Soc.
ISBN 13 : 0821891502
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Real Complexity and Computation by : Luis M. Pardo

Download or read book Recent Advances in Real Complexity and Computation written by Luis M. Pardo and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.

Orthogonal Polynomials

Author : Mama Foupouagnigni
Publisher : Springer Nature
ISBN 13 : 3030367444
Total Pages : 683 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni

Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.