Linear quintuple-product identities
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- by Richard Blecksmith and John Brillhart;
- Math. Comp. 72 (2003), 1019-1033
- DOI: https://doi.org/10.1090/S0025-5718-02-01461-8
- Published electronically: August 14, 2002
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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.References
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Bibliographic 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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1019-1033
- MSC (2000): Primary 11F11
- DOI: https://doi.org/10.1090/S0025-5718-02-01461-8
- MathSciNet review: 1954982
Dedicated: Dedicated to our longtime friend John Selfridge