The Ramanujan Journal

, Volume 7, Issue 1, pp 193–222

Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions

Authors

  • Basil Gordon
    • Department of MathematicsUniversity of California
  • Richard J. Mcintosh
    • Department of Mathematics and StatisticsUniversity of Regina
Article

DOI: 10.1023/A:1026299229509

Cite this article as:
Gordon, B. & Mcintosh, R.J. The Ramanujan Journal (2003) 7: 193. doi:10.1023/A:1026299229509

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 eir (r rational), there is a theta function Fr(q) with F(q) − Fr(q) = O(1). In this paper we obtain the transformations of Ramanujan's fifth and seventh order mock theta functions under the modular group generators τ → τ + 1 and τ → −1/τ, where q = eπiτ. The transformation formulas are more complex than those of ordinary theta functions. A definition of the order of a mock theta function is also given.

mock theta functionmodular formMordell integral

Copyright information

© Kluwer Academic Publishers 2003