Abstract
We give expressions for the Serre derivatives of Eisenstein and Poincaré series as well as their Rankin–Cohen brackets with arbitrary modular forms in terms of the Poincaré averaging construction, and derive several identities for the Ramanujan tau function as applications.
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Author's contributions
Acknowlegements
I thank the reviewers for pointing out a mistake in Remark 6 in an earlier version of this note, and also for several suggestions that improved the exposition.
