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The Ramanujan Journal

, Volume 24, Issue 3, pp 345–386 | Cite as

The basic bilateral hypergeometric series and the mock theta functions

  • Youn-Seo ChoiEmail author
Article

Abstract

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.

Keywords

Mock theta function The bilateral hypergeometric series Ramanujan 

Mathematics Subject Classification (2000)

33D15 11F27 33D99 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of MathematicsKIASSeoulKorea

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