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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Linear quintuple-product identities


Authors: Richard Blecksmith and John Brillhart
Journal: Math. Comp. 72 (2003), 1019-1033
MSC (2000): Primary 11F11
Published electronically: August 14, 2002
MathSciNet review: 1954982
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Abstract | References | Similar Articles | Additional Information

Abstract: In the first part of this paper, series and product representations of four single-variable triple products $T_0$, $T_1$, $T_2$, $T_3$ and four single-variable quintuple products $Q_0$, $Q_1$, $Q_2$, $Q_3$ are defined. Reduced forms and reduction formulas for these eight functions are given, along with formulas which connect them. The second part of the paper contains a systematic computer search for linear trinomial $Q$ identities. The complete set of such families is found to consist of two 2-parameter families, which are proved using the formulas in the first part of the paper.


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Additional Information

Richard Blecksmith
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: richard@math.niu.edu

John Brillhart
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: jdb@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01461-8
PII: S 0025-5718(02)01461-8
Keywords: Triple product, quintuple product, linear identity, search algorithm
Received by editor(s): August 29, 2001
Published electronically: August 14, 2002
Additional Notes: Research was supported in part by Northern Illinois University Research and Artistry grant
Dedicated: Dedicated to our longtime friend John Selfridge
Article copyright: © Copyright 2002 American Mathematical Society