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Orthogonal Polynomials and Special Functions

2006-06-19 Mathematics
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Release : 2006-06-19
Genre : Mathematics
Kind : eBook
Book Rating : 622/5 ( reviews)

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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. This book was released on 2006-06-19. 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

1975-06-01 Mathematics
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Release : 1975-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 189/5 ( reviews)

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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. This book was released on 1975-06-01. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.

Lectures on Orthogonal Polynomials and Special Functions

2020-10-15 Mathematics
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Release : 2020-10-15
Genre : Mathematics
Kind : eBook
Book Rating : 420/5 ( reviews)

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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. This book was released on 2020-10-15. 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 and Orthogonal Polynomials

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 909/5 ( reviews)

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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. This book was released on 2006. 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

2011-02-17 Mathematics
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Release : 2011-02-17
Genre : Mathematics
Kind : eBook
Book Rating : 293/5 ( reviews)

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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. This book was released on 2011-02-17. 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"--

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