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Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics : Developments in Mathematics - Frank G. Garvan

Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics

Developments in Mathematics

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

Hardcover Published: 30th November 2001
ISBN: 9781402001017
Number Of Pages: 286

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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.

Gaussian hypergeometric series and combinatorial congruencesp. 1
A double bounded key identity for Gollnitz's (BIG) partition theoremp. 13
Engel expansions of q-series by computer algebrap. 33
Sums of squares and the preservation of modularity under congruence restrictionsp. 59
On the transformation formula for the Dedekind eta-functionp. 73
Experiments and discoveries in q-trigonometryp. 79
Algebraic consequences of Jacobi's two- and four-square theoremsp. 107
The Borweins' cubic theta functions and q-elliptic functionsp. 133
Some Eisenstein series identities associated with the Borwein functionsp. 147
Hankel determinants of Eisenstein seriesp. 171
Jacobi's identity and two K3-surfacesp. 189
q-Random matrix ensemblesp. 199
Differential endomorphisms for modular formsp. 223
On the asymptotics of Takeuchi numbersp. 231
Fine-Tuning Zeilberger's Algorithm: The Methods of Automatic Filtering and Creative Substitutingp. 243
Gaussian integrals and the Rogers-Ramanujan identitiesp. 255
Some remarks on a product expansion: an unexplored partition functionp. 267
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781402001017
ISBN-10: 1402001010
Series: Developments in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 286
Published: 30th November 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.32