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.
Author(s): Scott Ahlgren (auth.), Frank G. Garvan, Mourad E. H. Ismail (eds.)
Series: Developments in Mathematics 4
Edition: 1
Publisher: Springer US
Year: 2001
Language: English
Pages: 286
Tags: Numeric Computing; Algebra; Combinatorics; Special Functions; Applications of Mathematics
Front Matter....Pages i-xi
Gaussian Hypergeometric Series and Combinatorial Congruences....Pages 1-12
A Double Bounded Key Identity for Göllnitz’s (BIG) Partition Theorem....Pages 13-32
Engel Expansions of q-Series by Computer Algebra....Pages 33-57
Sums of Squares and the Preservation of Modularity under Congruence Restrictions....Pages 59-71
On the Transformation Formula for the Dedekind Eta-Function....Pages 73-77
Experiments and Discoveries in q-Trigonometry....Pages 79-105
Algebraic Consequences of Jacobi’s Two— and Four—Square Theorems....Pages 107-132
The Borweins’ Cubic Theta Functions and q-Elliptic Functions....Pages 133-145
Some Eisenstein Series Identities Associated with the Borwein Functions....Pages 147-169
Hankel Determinants of Eisenstein Series....Pages 171-188
Jacobi’s Identity and Two K 3-Surfaces....Pages 189-198
q -Random Matrix Ensembles....Pages 199-221
Differential Endomorphisms for Modular Forms On Γ 0 (4)....Pages 223-229
On the Asymptotics of Takeuchi Numbers....Pages 231-242
Fine-Tuning Zeilberger’s Algorithm....Pages 243-254
Gaussian Integrals and the Rogers-Ramanujan Identities....Pages 255-265
Some Remarks on a Product Expansion....Pages 267-283
Back Matter....Pages 285-285
