Linear quintuple-product identities

In the first part of this paper, series and product representations of four single-variable triple products T0, T1, T2, T3 and four single-variable quintuple products Q0, Q1, Q2, Q3 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.