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Journal of Symbolic Computation
Volume 37, Issue 4, April 2004, Pages 415-448
 
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doi:10.1016/j.jsc.2003.04.002    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2003 Elsevier Ltd. All rights reserved.

RRtools—a Maple package for aiding the discovery and proof of finite Rogers–Ramanujan type identities

Andrew V. Sills Corresponding Author Contact Information, E-mail The Corresponding Author, E-mail The Corresponding Author

Department of Mathematics, Rutgers University, 110 Frelinghuysen RoadHill Center, Busch Campus, 08854-8019, Piscataway, NJ, USA

Received 24 September 2002; 
accepted 30 April 2003. 
Available online 20 February 2004.

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Abstract

The purpose of this paper is to introduce the RRtools and recpf Maple packages which were developed by the author to assist in the discovery and proof of finitizations of identities of the Rogers–Ramanujan type.

Author Keywords: Author Keywords: Rogers–Ramanujan identities; q-series; Experimental mathematics

Article Outline

1. Introduction
2. Mathematical preliminaries
2.1. q-binomial coefficients
2.2. q-trinomial coefficients
2.2.1. Definitions
2.2.2. Recurrences
2.2.3. Identities
2.2.4. Asymptotics
2.3. Miscellaneous results
3. Finitization and duality for Rogers–Ramanujan type identities
3.1. Finitization by the method of Image -difference equations
3.2. An example done “by hand”
3.3. Duality
4. The RRtools Maple package
4.1. Set-up and initialization
4.2. Basic Image -functions
4.3. Image -difference equations and recurrences
4.4. Conjecturing a finitization
4.4.1. Calculating a fermionic form
4.4.2. Conjecturing a bosonic form
4.5. Tools for duality
4.6. -shift operator algebraic procedures
5. A user’s guide to the recpf Maple package
5.1. Set-up and initialization
5.2. Overview
5.3. Demonstrations
5.3.1. Proof of a Image -trinomial identity
5.3.2. Proof of a finite second Rogers–Ramanujan identity
Acknowledgements
References

 
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