Linear quintuple-product identities

Authors:
Richard Blecksmith and John Brillhart

Journal:
Math. Comp. **72** (2003), 1019-1033

MSC (2000):
Primary 11F11

DOI:
https://doi.org/10.1090/S0025-5718-02-01461-8

Published electronically:
August 14, 2002

MathSciNet review:
1954982

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the first part of this paper, series and product representations of four single-variable triple products , , , and four single-variable quintuple products , , , 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 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:
https://doi.org/10.1090/S0025-5718-02-01461-8

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