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Encyclopedia Of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions
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Book Synopsis Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions by : Tom H. Koornwinder
Download or read book Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions written by Tom H. Koornwinder and published by Cambridge University Press. This book was released on 2020-10-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Encyclopedia of Special Functions: The Askey-Bateman Project by : Tom H. Koornwinder
Download or read book Encyclopedia of Special Functions: The Askey-Bateman Project written by Tom H. Koornwinder and published by Cambridge University Press. This book was released on 2020-09-30 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Bounded Littlewood Identities by : Eric M. Rains
Download or read book Bounded Littlewood Identities written by Eric M. Rains and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Orthogonal Polynomials of Several Variables by : Charles F. Dunkl
Download or read book Orthogonal Polynomials of Several Variables written by Charles F. Dunkl and published by Cambridge University Press. This book was released on 2014-08-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Book Synopsis Special Functions by : George E. Andrews
Download or read book Special Functions written by George E. Andrews and published by . This book was released on 2014-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.
Book Synopsis Special Functions by : George E. Andrews
Download or read book Special Functions written by George E. Andrews and published by Cambridge University Press. This book was released on 1999 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Book Synopsis Special Functions by : George E. Andrews
Download or read book Special Functions written by George E. Andrews and published by . This book was released on 1999 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Special Functions and Their Approximations by : Yudell L. Luke
Download or read book The Special Functions and Their Approximations written by Yudell L. Luke and published by Academic Press. This book was released on 1969 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.
Book Synopsis An Essay Toward a Unified Theory of Special Functions by : Clifford Truesdell
Download or read book An Essay Toward a Unified Theory of Special Functions written by Clifford Truesdell and published by Princeton University Press. This book was released on 1949-01-20 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford Truesdell’s classic essay on special functions from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Book Synopsis Hypergeometric Orthogonal Polynomials and Their q-Analogues by : Roelof Koekoek
Download or read book Hypergeometric Orthogonal Polynomials and Their q-Analogues written by Roelof Koekoek and published by Springer Science & Business Media. This book was released on 2010-03-18 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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]).
Book Synopsis Integrals and Series by : Anatolij P. Prudnikov
Download or read book Integrals and Series written by Anatolij P. Prudnikov and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Wavelets: An Elementary Treatment of Theory and Applications by : Tom H Koornwinder
Download or read book Wavelets: An Elementary Treatment of Theory and Applications written by Tom H Koornwinder and published by World Scientific. This book was released on 1993-06-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet bases adapted to inhomogeneous cases. Contents:Wavelets: First Steps (N M Temme)Wavelets: Mathematical Preliminaries (P W Hemker et al.)The Continuous Wavelet Transform (T H Koornwinder)Discrete Wavelets and Multiresolution Analysis (H J A M Heijmans)Image Compression Using Wavelets (P Nacken)Computing with Daubechies' Wavelets (A B Olde Daalhuis)Wavelet Bases Adapted to Inhomogeneous Cases (P W Hemker & F Plantevin)Conjugate Quadrature Filters for Multiresolution Analysis and Synthesis (E H Dooijes)Calculation of the Wavelet Decomposition Using Quadrature Formulae (W Sweldens & R Piessens)Fast Wavelet Transforms and Calderón-Zygmund Operators (T H Koornwinder)The Finite Wavelet Transform with an Application to Seismic Processing (J A H Alkemade)Wavelets Understand Fractals (M Hazewinkel) Readership: Applied mathematicians, numerical analysts, physicists, electrical engineers and signal analysts (sounds, images). Keywords:Wavelets;Continuous Wavelet Transform;Multiresolution Analysis;Daubechies Wavelets;Wavelet Bases;Calderon-Zygmund Operators;Conjugate Quadrature Filters;Image Compression;Seismic Processing;FractalsReviews: “… highly recommended to everyone who needs a quick account of wavelet theory as well as some ideas of wavelet applications. Results and basic theorems are stated in a rigorous and very satisfactory way, without overloading the treatment by including too many concisely worked-out proofs. Those interested in a more complete treatment will find enough hints on where to look up the details. While not being a textbook for students at an intermediate level, it can be useful as an aid in more advanced courses or seminars. For specialists in the field, the book can serve as a nice reference work; engineers and other people interested in algorithms for the fast wavelet transform will find it a useful guide to go directly to their specific interests. I am convinced that this ‘elementary treatment of theory and applications’ will become a standard reference for a broad audience.” Journal of Approximation Theory “As well as many exercises and remarks one finds lists of references after each chapter. These make the book valuable not only for graduate students but also for researchers.” European Maths. Soc. Newsletter
Book Synopsis Approximation Theory and Harmonic Analysis on Spheres and Balls by : Feng Dai
Download or read book Approximation Theory and Harmonic Analysis on Spheres and Balls written by Feng Dai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Book Synopsis The Andrews Festschrift by : Dominique Foata
Download or read book The Andrews Festschrift written by Dominique Foata and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Sminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus.
Book Synopsis Fractional Differential Equations by : Anatoly Kochubei
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Book Synopsis Special Functions and Their Applications by : Nikolaĭ Nikolaevich Lebedev
Download or read book Special Functions and Their Applications written by Nikolaĭ Nikolaevich Lebedev and published by . This book was released on 1965 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Functions and Orthogonal Polynomials by : Diego Dominici
Download or read book Special Functions and Orthogonal Polynomials written by Diego Dominici and published by American Mathematical Soc.. This book was released on 2008-10-16 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
