Hypergeometric Orthogonal Polynomials And Their Q Analogues

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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]).

Hypergeometric Orthogonal Polynomials And Their Q Analogues

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Author : Roelof Koekoek
language : en
Publisher: Springer
Release Date : 2010-10-22

Hypergeometric Orthogonal Polynomials And Their Q Analogues written by Roelof Koekoek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-22 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]).

Lectures On Orthogonal Polynomials And Special Functions

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Author : Howard S. Cohl
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15

Lectures On Orthogonal Polynomials And Special Functions written by Howard S. Cohl 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 2020-10-15 with Mathematics categories.

Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.

Hypergeometric Summation

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Author : Wolfram Koepf
language : en
Publisher: Springer
Release Date : 2014-06-10

Hypergeometric Summation written by Wolfram Koepf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Computers categories.

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system MapleTM. The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.

Some Basic Hypergeometric Orthogonal Polynomials That Generalize Jacobi Polynomials

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Author : Richard Askey
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Some Basic Hypergeometric Orthogonal Polynomials That Generalize Jacobi Polynomials written by Richard Askey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

A very general set of orthogonal polynomials in one variable that extends the classical polynomials is a set we called the q-Racah polynomials. In an earlier paper we gave the orthogonality relation for these polynomials when the orthogonality is purely discrete. We now give the weight function in the general case and a number of other properties of these very interesting orthogonal polynomials.

Orthogonal Polynomials And Special Functions

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Author : Kenier Castillo
language : en
Publisher: Springer Nature
Release Date : 2024-12-27

Orthogonal Polynomials And Special Functions written by Kenier Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-27 with Mathematics categories.

The aim of this book is to honor the memory of Professor José Carlos Petronilho and hence focuses on his main research areas (Special Functions, Orthogonal Polynomials, Approximation Theory). It is a collaborative book and among the contributing authors are outstanding leaders in the field. The book addresses different topics exploring the connection between the areas already mentioned and their applications, from different perspectives and using several tools, both analytical and algebraic. Beside the researches working in these topics, the book potentially interests the readers working in areas of Mathematics, Science and Technology where Approximation Theory, Special Functions and Orthogonality are potentially useful tools.

Classical Hypergeometric Functions And Generalizations

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Author : Howard S. Cohl
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-23

Classical Hypergeometric Functions And Generalizations written by Howard S. Cohl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.

This is the first volume of a two-volume collection of recent research results related to hypergeometric functions. The second volume (Contemporary Mathematics, Volume 819) is titled Applications and $q$-Extensions of Hypergeometric Functions. This volume contains the proceedings of a minisymposium and two AMS special sessions in three conferences: Minisymposium on All Things Hypergeometric, $q$-series and Generalizations at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), June 13–17, 2022, Centre de Recherches Mathématiques, Montréal, Québec, Canada; AMS Special Session on Hypergeometric Functions and $q$-series at the 2022 AMS Fall Western Sectional Meeting, October 22–23, 2022, University of Utah, Salt Lake City, Utah; and the AMS Special Session on Hypergeometric Functions, $q$-series and Generalizations, at the 2023 AMS Spring Eastern Virtual Sectional Meeting, April 1–2, 2023. This book provides a sampling of current mathematical research related to the Gauss hypergeometric function, and as well, its immediate generalizations and extensions. This includes the generalized hypergeometric functions that originated with Kummer, as well as such classical special functions as Lamé and Heun functions. It also includes certain functions relevant to algebraic geometry, such as hypergeometric functions over finite fields. All research articles come with extensive bibliographies and can serve as entry points to the current literature.

Special Functions And Orthogonal Polynomials

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Author : Richard Beals
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-17

Special Functions And Orthogonal Polynomials written by Richard Beals 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 2016-05-17 with Mathematics categories.

A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.

Orthogonal Polynomials

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Author : Mama Foupouagnigni
language : en
Publisher: Springer Nature
Release Date : 2020-03-11

Orthogonal Polynomials written by Mama Foupouagnigni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.

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.

Canadian Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1996-02

Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02 with categories.