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On An Identity Of Gessel And Stanton And The New Little Göllnitz Identities, Carla D. Savage, Andrew Sills

Department of Mathematical Sciences Faculty Publications

We show that an identity of Gessel and Stanton [I. Gessel, D. Stanton, Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983) 197, Eq. (7.24)] can be viewed as a symmetric version of a recent analytic variation of the little Göllnitz identities. This is significant, since the Göllnitz–Gordon identities are considered the usual symmetric counterpart to little Göllnitz theorems. Is it possible, then, that the Gessel–Stanton identity is part of an infinite family of identities like those of Göllnitz–Gordon?

Toward this end, we derive partners and generalizations of the Gessel–Stanton identity. We show that …