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The generating series of Gromov-Witten invariants of elliptic curves can beexpressed in terms of multi-variable elliptic functions by works ofBloch-Okounkov and Okounkov-Pandharipande. In this work we give newsum-over-partitions formulas for these generating series and show that they areconfiguration space integrals of cohomology classes constructed from sectionsof Poincare bundles. We also discuss their quasi-elliptic and quasi-modularproperties.

Gromov-Witten Generating Series of Elliptic Curves as Configuration Space Integrals