Linear quintuple-product identities

Blecksmith, Richard; Brillhart, John

doi:10.1090/S0025-5718-02-01461-8

Linear quintuple-product identities
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by Richard Blecksmith and John Brillhart PDF

Math. Comp. 72 (2003), 1019-1033 Request permission

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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