Developments in Mathematics

By: Frank G. Garvan (Editor), Mourad E.H. Ismail (Editor)

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Hardcover | 30 November 2001

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300 Pages

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These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999. The main emphasis of the conference was Com puter Algebra (i. e. symbolic computation) and how it related to the fields of Number Theory, Special Functions, Physics and Combinatorics. A subject that is common to all of these fields is q-series. We brought together those who do symbolic computation with q-series and those who need q-series in cluding workers in Physics and Combinatorics. The goal of the conference was to inform mathematicians and physicists who use q-series of the latest developments in the field of q-series and especially how symbolic computa tion has aided these developments. Over 60 people were invited to participate in the conference. We ended up having 45 participants at the conference, including six one hour plenary speakers and 28 half hour speakers. There were talks in all the areas we were hoping for. There were three software demonstrations.

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You Can Find This Book In

Non-Fiction Mathematics Number Theory Combinatorics & Graph Theory Algebra Science Physics Mathematical Physics Geometry Probability & Statistics Computing & I.T.Computer Science

Mathematical Theory of Computation Medicine Medicine in General Applied Mathematics Calculus & Mathematical Analysis Numerical Analysis

Preface
Participants
Gaussian hypergeometric series and combinatorial congruences	p. 1
A double bounded key identity for Gollnitz's (BIG) partition theorem	p. 13
Engel expansions of q-series by computer algebra	p. 33
Sums of squares and the preservation of modularity under congruence restrictions	p. 59
On the transformation formula for the Dedekind eta-function	p. 73
Experiments and discoveries in q-trigonometry	p. 79
Algebraic consequences of Jacobi's two- and four-square theorems	p. 107
The Borweins' cubic theta functions and q-elliptic functions	p. 133
Some Eisenstein series identities associated with the Borwein functions	p. 147
Hankel determinants of Eisenstein series	p. 171
Jacobi's identity and two K3-surfaces	p. 189
q-Random matrix ensembles	p. 199
Differential endomorphisms for modular forms	p. 223
On the asymptotics of Takeuchi numbers	p. 231
Fine-Tuning Zeilberger's Algorithm: The Methods of Automatic Filtering and Creative Substituting	p. 243
Gaussian integrals and the Rogers-Ramanujan identities	p. 255
Some remarks on a product expansion: an unexplored partition function	p. 267
Table of Contents provided by Blackwell. All Rights Reserved.

Developments in Mathematics

At a Glance

Hardcover

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