= Weak modular form
= Weakly modular holomorphic function
{synonym}
Here a weak modular form is a <holomorphic function> on the <complex upper half-plane> satisfying the weight-$k$ transformation law, with no growth condition at any <cusp of a modular group>. This convention differs from weakly holomorphic modular forms, which are required to be meromorphic at the cusps. At level one, translation invariance gives a Laurent expansion on the punctured unit disc, possibly with infinitely many negative powers.
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