COMPOSITION-THEORETIC SERIES AND FALSE THETA FUNCTIONS

Many natural partition-theoretic series can be equally readily interpreted as compo-sition-theoretic series, but this viewpoint seems to have not been much employed in either theory. We consider some of the consequences of this viewpoint. As examples, we give results concerning the reciprocals of Ramanujan’s theta functions and of the false theta functions of L. J. Rogers, and raise an array of questions related to these. Part of this study may be considered a natural dual of the truncated pentagonal number theorem of Andrews and Merca.