S. Ramanujan introduced the mock theta functions in his last letter to G.H. Hardy. In his letter and Lost Notebook, he presented mock theta functions and their identities. The expression of each mock theta function relies on the hypergeometric series. G.N. Watson studied the relations between Ramanujan’s fifth order mock theta functions and the function introduced by M. Lerch in 1893. In this manuscript, we develop the relations between the basic bilateral hypergeometric series and the functions deduced from all mock theta functions introduced by G.E. Andrews, B.C. Berndt, S.H. Chan, R. McIntosh, Ramanujan, and Watson.
Mock theta function The bilateral hypergeometric series Ramanujan
Mathematics Subject Classification (2000)
33D15 11F27 33D99
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