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In the present paper, we introduce the notion of nearly holomorphic Drinfeldmodular forms and study an analogue of Maass-Shimura operators in this context.Furthermore, for a given nearly holomorphic Drinfeld modular form, we show thatits special values at CM points are algebraically independent whenever theassociated endomorphism algebras are distinct. As an application of our resultson nearly holomorphic Drinfeld modular forms, we study Drinfeld quasi-modularforms for arbitrary congruence subgroups and investigate the structure of thevector spaces and the algebras generated by them.

Nearly holomorphic Drinfeld modular forms and their special values at CM points