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The Ramanujan Journal

, Volume 48, Issue 3, pp 613–622 | Cite as

Some identities associated with mock theta functions \(\omega (q)\) and \(\nu (q)\)

  • George E. Andrews
  • Ae Ja YeeEmail author
Article

Abstract

Recently, Andrews, Dixit, and Yee defined two partition functions \(p_{\omega }(n)\) and \(p_{\nu }(n)\) that are related with Ramanujan’s mock theta functions \(\omega (q)\) and \(\nu (q)\), respectively. In this paper, we present two variable generalizations of their results. As an application, we reprove their results on \(p_{\omega }(n)\) and \(p_{\nu }(n)\) that are analogous to Euler’s pentagonal number theorem.

Keywords

Partitions Mock theta functions \(\omega (q)\) and \(\nu (q)\) Euler’s pentagonal number theorem 

Mathematics Subject Classification

Primary 05A17 Secondary 11P81 

Notes

Acknowledgements

The authors would like to thank the referee for his/her careful reading and valuable comments.

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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