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

Abstract

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

12 pages

References in corpus (1)

• On the Mahler measure of $1+X+1/X+Y+1/Y$