Overview

This volume contains research and expository papers in a number of different topics including number theory, special functions, physics and combinatorics. A subject that is common to all of these fields is q-series. The chapters contain some of the latest developments in the fields of q-series. Some of the papers describe how symbolic computation has aided these developments. This volume is intended for researchers and graduate students interested in recent developments in q-series and symbolic computation.

Full Product Details

Author:   Frank G. Garvan ,  Mourad E.H. Ismail
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2002 ed.
Volume:   4
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.320kg
ISBN:  

9781402001017

ISBN 10:   1402001010
Pages:   286
Publication Date:   30 November 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Gaussian hypergeometric series and combinatorial congruences.- A double bounded key identity for Göllnitz’s (BIG) partition theorem.- Engel expansions of q-series by computer algebra.- Sums of squares and the preservation of modularity under congruence restrictions.- On the transformation formula for the Dedekind eta-function.- Experiments and discoveries in q-trigonometry.- Algebraic consequences of Jacobi’s two— and four—square theorems.- The Borweins’ cubic theta functions and q-elliptic functions.- Some Eisenstein series identities associated with the Borwein functions.- Hankel determinants of Eisenstein series.- Jacobi’s identity and two K3-surfaces.- q-Random matrix ensembles.- Differential endomorphisms for modular forms.- On the asymptotics of Takeuchi numbers.- Fine-Tuning Zeilberger’s Algorithm: The Methods of Automatic Filtering and Creative Substituting.- Gaussian integrals and the Rogers-Ramanujan identities.- Some remarks on a product expansion: an unexplored partition function.

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