The Ramanujan Journal

, Volume 14, Issue 1, pp 173–188

The Bailey transform and false theta functions



An empirical exploration of five of Ramanujan's intriguing false theta function identities leads to unexpected instances of Bailey's transform which, in turn, lead to many new identities for both false and partial theta functions.


Ramanujan False theta series Bailey transform Bailey pair 


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  1. 1.
    Andrews, G.E.: The theory of partitions. Encycl. of Math. and Its Appl., vol. 2, Addison-Wesley, Reading, 1976. (Reissued:Cambridge University Press, 1985)Google Scholar
  2. 2.
    Andrews, G.E.: Multiple series Rogers–Ramanujan type identities. Pacific J. Math. 114, 267–283 (1984)MATHMathSciNetGoogle Scholar
  3. 3.
    Andrews, G.E.: Bailey's transform, lemma, chains and tree. In: Bustoz et al. J. (eds.) Special Functions 2000: Current Perspective and Future Directions, pp. 1–22. Dordrecht, Kluwer Academic Publishers (2001)Google Scholar
  4. 4.
    Andrews, G.E., Berndt, B.C.: Ramanujan's lost notebook, vol. 1, Springer, New York (2005) Google Scholar
  5. 5.
    Bailey, W.N.: Identities of the Rogers-Ramanujan type. Proc. London Math. Soc. 50(2), 1–10 (1949)MathSciNetGoogle Scholar
  6. 6.
    Bressoud, D.M.: Some identities for terminating q-series. Math. Proc. Camb. Phil. Soc. 89, 211–223 (1981).MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Fine, N.J.: Basic hypergeometric series and applications. Mathematical Surveys and Monographs, Vol. 27, AMS, Providence, Rhode Island (1888) Google Scholar
  8. 8.
    Gasper, G., Rahman, M.: Basic hypergeometric series, 2nd ed., Encycl. of Math and Its Appl., vol. 96,Cambridge University Press, Cambridge (2004)Google Scholar
  9. 9.
    Ramanujan, S.: The Lost Notebook and Other Unpublished Papers}. Narosa, New Delhi (1988)Google Scholar
  10. 10.
    Rogers, L.J.: On two theorems of combinatory analysis and some allied identities. Proc. London Math. Soc. 16(2), 315–336 (1917).Google Scholar
  11. 11.
    Schilling, A., Warnaar, S.O.: A higher level Bailey lemma: proof and application. Ramanujan J. 2, 327–349 (1998)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Schilling, A., Warnaar, S.O.: Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma. Contemp. Math. 297, 227–255 (2002)MathSciNetGoogle Scholar
  13. 13.
    Singh, U.B.: A note on a transformation of Bailey. Quart. J. Math. Oxford Ser. 45(2), 111–116 (1994)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Slater, L.J.: A new proof of Rogers' transformations of infinite series. Proc. London Math. Soc. 53(2), 460–475 (1951)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Slater, L.J.: Further identities of the Rogers–Ramanujan type. Proc. London Math. Soc.54(2), 147–167 (1952)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Slater, L.J.: Generalized Hypergeometric Functions. Cambridge University Press, Cambridge (1966)Google Scholar
  17. 17.
    Warnaar, S.O.: 50 Years of Bailey's lemma. In: A. Betten et al. (eds.) Algebraic Combinatorics and Applications, PP. 333–347. Springer, Berlin (2001)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of Mathematics and StatisticsThe University of MelbourneMelbourneAustralia

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