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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: 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

John Brillhart
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721

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