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An Introduction To Orthogonal Polynomials

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An Introduction To Orthogonal Polynomials

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Author : Theodore S Chihara
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17

An Introduction To Orthogonal Polynomials written by Theodore S Chihara and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.

"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"--

An Introduction To Orthogonal Polynomials

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Author : Theodore S Chihara
language : en
Publisher: Courier Corporation
Release Date : 2014-07-01

Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. 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. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.

Orthogonal Polynomials Of Several Variables

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Author : Charles F. Dunkl
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-21

Orthogonal Polynomials Of Several Variables written by Charles F. Dunkl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-21 with Mathematics categories.

Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.

An Introduction To Orthogonal Polynomials

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Author : Theodore Seio Chihara
language : en
Publisher:
Release Date : 2014-01-01

An Introduction To Orthogonal Polynomials written by Theodore Seio Chihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Functions, Orthogonal categories.

The Classical Orthogonal Polynomials

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Author : Brian George Spencer Doman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-09-18

The Classical Orthogonal Polynomials written by Brian George Spencer Doman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.

This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have. The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation. Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.

Orthogonal Polynomials In The Spectral Analysis Of Markov Processes

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Author : Manuel Domínguez de la Iglesia
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-21

Orthogonal Polynomials In The Spectral Analysis Of Markov Processes written by Manuel Domínguez de la Iglesia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-21 with Mathematics categories.

In pioneering work in the 1950s, S. Karlin and J. McGregor showed that probabilistic aspects of certain Markov processes can be studied by analyzing orthogonal eigenfunctions of associated operators. In the decades since, many authors have extended and deepened this surprising connection between orthogonal polynomials and stochastic processes. This book gives a comprehensive analysis of the spectral representation of the most important one-dimensional Markov processes, namely discrete-time birth-death chains, birth-death processes and diffusion processes. It brings together the main results from the extensive literature on the topic with detailed examples and applications. Also featuring an introduction to the basic theory of orthogonal polynomials and a selection of exercises at the end of each chapter, it is suitable for graduate students with a solid background in stochastic processes as well as researchers in orthogonal polynomials and special functions who want to learn about applications of their work to probability.

Orthogonal Polynomials

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Author : Walter Gautschi
language : en
Publisher: Oxford University Press on Demand
Release Date : 2004

Orthogonal Polynomials written by Walter Gautschi and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

Introduction To The Theory Of Weighted Polynomial Approximation

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Author : Hrushikesh Narhar Mhaskar
language : en
Publisher: World Scientific
Release Date : 1996

Introduction To The Theory Of Weighted Polynomial Approximation written by Hrushikesh Narhar Mhaskar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Orthogonal Polynomials And Special Functions

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Author : Richard Askey
language : en
Publisher: SIAM
Release Date : 1975-06-01

Orthogonal Polynomials And Special Functions written by Richard Askey and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-06-01 with Mathematics categories.

This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.

Discrete Orthogonal Polynomials

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Author : Jinho Baik
language : en
Publisher:
Release Date : 2007

Discrete Orthogonal Polynomials written by Jinho Baik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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An Introduction To Orthogonal Polynomials

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