Special Functions and Orthogonal Polynomials

Author: Refaat El Attar

Publisher: Lulu.com

ISBN: 1411666909

Category: Mathematics

Page: 310

View: 1555

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(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.
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Special Functions 2000: Current Perspective and Future Directions

Author: Joaquin Bustoz,Mourad E.H. Ismail,Sergei Suslov

Publisher: Springer Science & Business Media

ISBN: 9401008183

Category: Mathematics

Page: 520

View: 9109

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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.
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Difference Equations, Special Functions and Orthogonal Polynomials

Proceedings of the International Conference, Munich, Germany, 25-30 July 2005

Author: Saber Elaydi

Publisher: World Scientific

ISBN: 9812706437

Category: Science

Page: 773

View: 7715

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This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
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Orthogonal Polynomials and Special Functions

Computation and Applications

Author: European summer school on orthogonal polynomials and special functions,Francisco Marcellàn

Publisher: Springer Science & Business Media

ISBN: 3540310622

Category: Mathematics

Page: 418

View: 1633

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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.
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Laredo Lectures on Orthogonal Polynomials and Special Functions

Author: Renato Alvarez-Nodarse,Francisco Marcellán,Walter van Assche

Publisher: Nova Publishers

ISBN: 9781594540097

Category: Mathematics

Page: 210

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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.
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Special Functions and Orthogonal Polynomials

AMS Special Session on Special Functions and Orthogonal Polynomials, April 21-22, 2007, Tucson, Arizona

Author: Diego Dominici,Robert Sullivan Maier

Publisher: American Mathematical Soc.

ISBN: 0821846507

Category: Mathematics

Page: 218

View: 5497

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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.
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Orthogonal Polynomials and Special Functions

Leuven 2002

Author: Erik Koelink,Walter Van Assche

Publisher: Springer

ISBN: 3540449450

Category: Mathematics

Page: 250

View: 2121

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

11th International Symposium, August 29-September 2, 2011, Universidad Carlos III de Madrid, Leganés, Spain

Author: Jorge Arvesœ,Guillermo Lopez Lagomasino

Publisher: American Mathematical Soc.

ISBN: 0821868969

Category: Mathematics

Page: 254

View: 342

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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.
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