The Classical Orthogonal Polynomials
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Classical And Quantum Orthogonal Polynomials In One Variable
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Author : Mourad Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-21
Classical And Quantum Orthogonal Polynomials In One Variable written by Mourad Ismail 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 2005-11-21 with Mathematics categories.
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
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.
The Classical Orthogonal Polynomials
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Author : Brian George Spencer Doman
language : en
Publisher: World Scientific
Release Date : 2015-09-18
The Classical Orthogonal Polynomials written by Brian George Spencer Doman and has been published by World Scientific 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.
Hypergeometric Orthogonal Polynomials And Their Q Analogues
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Author : Roelof Koekoek
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-18
Hypergeometric Orthogonal Polynomials And Their Q Analogues written by Roelof Koekoek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-18 with Mathematics categories.
The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).
Classical Orthogonal Polynomials Of A Discrete Variable
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Author : Arnold F. Nikiforov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Orthogonal Polynomials Of A Discrete Variable written by Arnold F. Nikiforov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.
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.
Applications And Computation Of Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-01
Applications And Computation Of Orthogonal Polynomials written by Walter Gautschi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-01 with Mathematics categories.
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.
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"--