Encyclopedia Of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions

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Encyclopedia Of Special Functions The Askey Bateman Project

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Author : Tom H. Koornwinder
language : en
Publisher:
Release Date : 2020

Encyclopedia Of Special Functions The Askey Bateman Project written by Tom H. Koornwinder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.

This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Encyclopedia Of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions

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Author : Tom H. Koornwinder
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15

Encyclopedia Of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions written by Tom H. Koornwinder 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.

This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Encyclopedia Of Special Functions The Askey Bateman Project

DOWNLOAD
Author : Tom H. Koornwinder
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15

Encyclopedia Of Special Functions The Askey Bateman Project written by Tom H. Koornwinder 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.

This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Bounded Littlewood Identities

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Author : Eric M. Rains
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21

Bounded Littlewood Identities written by Eric M. Rains 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 2021-07-21 with Education categories.

We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.

Macdonald Polynomials

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Author : Masatoshi Noumi
language : en
Publisher: Springer Nature
Release Date : 2023-09-08

Macdonald Polynomials written by Masatoshi Noumi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-08 with Science categories.

This book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021. Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the GLn version) as eigenfunctions of a q-difference operator, called the Macdonald–Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting q-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and q-Dunkl operators.

Special Functions

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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999

Special Functions written by George E. Andrews 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 1999 with Mathematics categories.

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

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]).

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.

Wavelets

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Author : T. H. Koornwinder
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1993

Wavelets written by T. H. Koornwinder and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.

Affine Hecke Algebras And Orthogonal Polynomials

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Author : I. G. Macdonald
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-20

Affine Hecke Algebras And Orthogonal Polynomials written by I. G. Macdonald 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 2003-03-20 with Mathematics categories.

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.