Encyclopedia Of Special Functions The Askey Bateman Project Volume 2 Multivariable Special Functions
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Author | : Tom H. Koornwinder |
Publisher | : Cambridge University Press |
Total Pages | : 442 |
Release | : 2020-10-15 |
Genre | : Mathematics |
ISBN | : 1108916554 |
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.
Author | : Tom H. Koornwinder |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 2020-09-30 |
Genre | : Mathematics |
ISBN | : 9781107003736 |
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.
Author | : George E. Andrews |
Publisher | : Cambridge University Press |
Total Pages | : 684 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780521789882 |
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Author | : Eric M. Rains |
Publisher | : American Mathematical Soc. |
Total Pages | : 115 |
Release | : 2021-07-21 |
Genre | : Education |
ISBN | : 1470446901 |
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.
Author | : George E. Andrews |
Publisher | : |
Total Pages | : |
Release | : 2014-01-01 |
Genre | : Functions, Special |
ISBN | : 9780521170222 |
This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.
Author | : Charles F. Dunkl |
Publisher | : Cambridge University Press |
Total Pages | : 439 |
Release | : 2014-08-21 |
Genre | : Mathematics |
ISBN | : 1107071895 |
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Author | : Mourad Ismail |
Publisher | : American Mathematical Soc. |
Total Pages | : 289 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 082180524X |
This book contains contributions from the proceedings at The Fields Institute workshop on Special Functions, q-Series and Related Topics that was held in June 1995. The articles cover areas from quantum groups and their representations, multivariate special functions, q-series, and symbolic algebra techniques as well as the traditional areas of single-variable special functions. The book contains both pure and applied topics and reflects recent trends of research in the various areas of special functions.
Author | : Mourad E. H. Ismail |
Publisher | : Springer Science & Business Media |
Total Pages | : 497 |
Release | : 2006-03-30 |
Genre | : Mathematics |
ISBN | : 0387242333 |
A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.
Author | : Z. X. Wang |
Publisher | : World Scientific |
Total Pages | : 720 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9789971506674 |
Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptotic expansion of functions. For physicists, engineers, and mathematicians. Acidic paper. Paper edition (unseen), $38. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Yury A. Brychkov |
Publisher | : CRC Press |
Total Pages | : 702 |
Release | : 2008-05-28 |
Genre | : Mathematics |
ISBN | : 158488956X |
Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.