Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

Bruce C. Berndt, George Lamb, Mathew Rogers

Published 2011-08-25, updated 2011-08-26Version 2

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers--Ramanujan continued fraction play central roles in our evaluations