 The technical condition to ensure that an infinite sum such as this converges to a meromorphic function is that on any compact set, after omitting the finitely many terms having poles in that set, the remaining series converges normally.On any compact disk defined by , and for any , one has

and it can be shown that the sum

converges regardless of .By writing as a Laurent series and explicitly comparing terms, one may verify that it satisfies the relation

where

and

This means that the pair parametrize an elliptic curve.