  The generating series of Gromov-Witten invariants of elliptic curves can be
expressed in terms of multi-variable elliptic functions by works of
Bloch-Okounkov and Okounkov-Pandharipande. In this work we give new
sum-over-partitions formulas for these generating series and show that they are
configuration space integrals of cohomology classes constructed from sections
of Poincare bundles. We also discuss their quasi-elliptic and quasi-modular
properties.
