Ramanujan's $_{1}ψ_1$ summation, Hecke-type double sums, and Appell-Lerch sums (1208.1359v1)

Abstract: We use a specialization of Ramanujan's ${}_1\psi_1$ summation to give a new proof of a recent formula of Hickerson and Mortenson which expands a special family of Hecke-type double sums in terms of Appell-Lerch sums and theta functions.