Unilateral and bilateral summation theorems in the theory of basic hypergeometric series

When/Where:

March 15, 2022, 1:55 — 2:45 pm at LIT 368.

Abstract:

 The ₆φ₅ summation theorem of L.J. Rogers has a formulation, due to F.H. Jackson, which is symmetrical with respect to three of its parameters. I will re-examine the problem, first considered by Jackson, of extending Rogers’s identity to one which possesses a fourfold symmetry. I will then provide some examples to demonstrate how the theory of elliptic functions may be used to convert certain unilateral summation theorems into bilateral summation theorems. The bilateral series considered will include those which feature in Ramanujan’s ₁ψ₁ identity and Bailey’s ₆ψ₆ identity, along with a few others which are similarly expressible as infinite products. Combinatorial interpretations of several q-series identities will also be given in terms of Ferrers diagrams.