We consider alternative orders of summation for the conditionally convergent series defining the weight-2 Eisenstein series and the Weierstrass -function. The resulting sums differ from the standard ones by a residual term that can be thought of as a function of the shapes with respect to which we sum. We compute this residual function explicitly and give some examples. The results generalize the well-known quasimodularity relationship between and its series summed in the reverse order.
"Alternative summation orders for the Eisenstein series $G_2$ and Weierstrass $\wp$-function." Rocky Mountain J. Math. 50 (4) 1473 - 1482, August 2020. https://doi.org/10.1216/rmj.2020.50.1473