Ramanujan's $_{1}\psi_1$ summation, Hecke-type double sums, and   Appell-Lerch sums
  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. 
Eric Mortenson
math.NT