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

1. Front Matter

   Pages i-xi

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2. Gaussian Hypergeometric Series and Combinatorial Congruences

   • Scott Ahlgren

   Pages 1-12

3. A Double Bounded Key Identity for Göllnitz’s (BIG) Partition Theorem

   • Krishnaswami Alladi, Alexander Berkovich

   Pages 13-32

4. Engel Expansions of q-Series by Computer Algebra

   • George E. Andrews, Arnold Knopfmacher, Peter Paule, Burkhard Zimmermann

   Pages 33-57

5. Sums of Squares and the Preservation of Modularity under Congruence Restrictions

   • Paul T. Bateman, Boris A. Datskovsky, Marvin I. Knopp

   Pages 59-71

6. On the Transformation Formula for the Dedekind Eta-Function

   • Bruce C. Berndt, K. Venkatachaliengar

   Pages 73-77

7. Experiments and Discoveries in q-Trigonometry

   • R. Wm. Gosper

   Pages 79-105

8. Algebraic Consequences of Jacobi’s Two— and Four—Square Theorems

   • Michael D. Hirschhorn, James A. McGowan

   Pages 107-132

9. The Borweins’ Cubic Theta Functions and q-Elliptic Functions

   • Richard Lewis, Zhi-Guo Liu

   Pages 133-145

10. Some Eisenstein Series Identities Associated with the Borwein Functions

    • Zhi-Guo Liu

    Pages 147-169

11. Hankel Determinants of Eisenstein Series

    • Stephen C. Milne

    Pages 171-188

12. Jacobi’s Identity and Two K3-Surfaces

    • Maki Murata

    Pages 189-198

13. q-Random Matrix Ensembles

    • K. A. Muttalib, Y. Chen, M. E. H. Ismail

    Pages 199-221

14. Differential Endomorphisms for Modular Forms On Γ0(4)

    • Ken Ono

    Pages 223-229

15. On the Asymptotics of Takeuchi Numbers

    • Thomas Prellberg

    Pages 231-242

16. Fine-Tuning Zeilberger’s Algorithm

    • Axel Riese

    Pages 243-254

17. Gaussian Integrals and the Rogers-Ramanujan Identities

    • D. Stanton

    Pages 255-265

18. Some Remarks on a Product Expansion

    • M. V. Subbarao, A. Verma

    Pages 267-283

19. Back Matter

    Pages 285-285

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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.

• algebra
• algorithms
• Combinatorics
• computer
• computer algebra
• elliptic function
• field
• Jacobi
• matrix
• modular form
• number theory
• Partition
• transformation

• Department of Mathematics, University of Florida, Gainesville, USA

  Frank G. Garvan

• Department of Mathematics, University of South Florida, Tampa, USA

  Mourad E. H. Ismail

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