Second Order Mock Theta Functions

Abstract

Abstract In his last letter to Hardy, Ramanujan defined 17 functions F ( q ), where | q | < 1. He called them mock theta functions, because as q radially approaches any point e 2 πir ( r rational), there is a theta function F r ( q ) with F ( q ) − Fr ( q ) = O (1). In this paper we establish the relationship between two families of mock theta functions.