Author: Tom H. Koornwinder
Publisher: Cambridge University Press
ISBN: 1108916554
Category : Mathematics
Languages : en
Pages : 442
Book Description
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
Author: Tom H. Koornwinder
Publisher: Cambridge University Press
ISBN: 1108916554
Category : Mathematics
Languages : en
Pages : 442
Book Description
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.
Publisher: Cambridge University Press
ISBN: 1108916554
Category : Mathematics
Languages : en
Pages : 442
Book Description
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
Author: Tom H. Koornwinder
Publisher: Cambridge University Press
ISBN: 9781107003736
Category : Mathematics
Languages : en
Pages : 433
Book Description
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.
Publisher: Cambridge University Press
ISBN: 9781107003736
Category : Mathematics
Languages : en
Pages : 433
Book Description
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
Author: Mourad E. H. Ismail
Publisher: Cambridge University Press
ISBN: 0521197422
Category : Mathematics
Languages : en
Pages : 0
Book Description
Extensive update of the Bateman Manuscript Project. Volume 1 covers orthogonal polynomials and moment problems.
Publisher: Cambridge University Press
ISBN: 0521197422
Category : Mathematics
Languages : en
Pages : 0
Book Description
Extensive update of the Bateman Manuscript Project. Volume 1 covers orthogonal polynomials and moment problems.
Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521789882
Category : Mathematics
Languages : en
Pages : 684
Book Description
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Publisher: Cambridge University Press
ISBN: 9780521789882
Category : Mathematics
Languages : en
Pages : 684
Book Description
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Orthogonal Polynomials of Several Variables
Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Bounded Littlewood Identities
Author: Eric M. Rains
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115
Book Description
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.
A First Course in Random Matrix Theory
Author: Marc Potters
Publisher: Cambridge University Press
ISBN: 1108488080
Category : Computers
Languages : en
Pages : 371
Book Description
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Publisher: Cambridge University Press
ISBN: 1108488080
Category : Computers
Languages : en
Pages : 371
Book Description
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Special Functions
Author: George E. Andrews
Publisher:
ISBN: 9780521170222
Category : Functions, Special
Languages : en
Pages :
Book Description
This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.
Publisher:
ISBN: 9780521170222
Category : Functions, Special
Languages : en
Pages :
Book Description
This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.
Special Functions and Orthogonal Polynomials
Author: Diego Dominici
Publisher: American Mathematical Soc.
ISBN: 0821846507
Category : Mathematics
Languages : en
Pages : 226
Book Description
"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.
Publisher: American Mathematical Soc.
ISBN: 0821846507
Category : Mathematics
Languages : en
Pages : 226
Book Description
"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.
A First Course in Fourier Analysis
Author: David W. Kammler
Publisher: Cambridge University Press
ISBN: 1139469037
Category : Mathematics
Languages : en
Pages : 39
Book Description
This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
Publisher: Cambridge University Press
ISBN: 1139469037
Category : Mathematics
Languages : en
Pages : 39
Book Description
This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.