Abstract
Residual identities of Ramanujan-type partial theta identities are tailor-made for producing conjugate Bailey pairs. This is carried out for partial theta identities in Ramanujan’s lost notebook, a number of the partial theta identities of Warnaar, and for some new ones as well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews, G.E.: Ramanujan’s “lost” notebook, I: partial theta functions. Adv. Math. 41, 137–172 (1981)
Andrews, G.E.: The fifth and seventh order mock theta functions. Trans. Am. Math. Soc. 293, 113–134 (1986)
Andrews, G.E.: q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra. C.B.M.S. Regional Conference Series in Math, vol. 66. American Math. Soc., Providence (1986)
Andrews, G.E.: Bailey chains and generalized Lambert series: I. Four identities of Ramanujan. Ill. J. Math. 36, 251–274 (1992)
Andrews, G.E., Dyson, F.J., Hickerson, D.: Partitions and indefinite quadratic forms. Invent. Math. 91, 391–407 (1988)
Andrews, G.E., Hickerson, D.: Ramanujan’s “lost” notebook, VII: The sixth order mock theta functions. Adv. Math. 89, 60–105 (1991)
Andrews, G.E., Warnaar, S.O.: The Bailey transform and false theta functions. Ramanujan J. 14, 173–188 (2007)
Bailey, W.N.: Identities of the Rogers–Ramanujan type. Proc. Lond. Math. Soc. 50, 1–10 (1949)
Berndt, B.C., Andrews, G.E.: Ramanujan’s Lost Notebook Part II. Springer, New York (2009)
Bressoud, D.M.: Some identities for terminating q-series. Math. Proc. Camb. Philos. Soc. 89, 211–223 (1981)
Conley, C.H., Raum, M.: Harmonic Maass–Jacobi forms of degree 1 with higher rank indices. Preprint
Fine, N.: Basic Hypergeometric Series and Applications. American Mathematical Society, Providence (1988)
Gasper, G., Rahman, M.: Basic Hypergeometric Series, 2nd edn. Cambridge University Press, Cambridge (2004)
Hickerson, D., Mortenson, E.: Hecke-type double sums, Appell–Lerch sums, and mock theta functions (I). Preprint
Hikami, K.: Hecke type formula for unified Witten–Reshetikhin–Turaev invariants as higher-order mock theta functions. Int. Math. Res. Not., rnm022 (2007)
Lovejoy, J.: Lacunary partition functions. Math. Res. Lett. 9, 191–198 (2002)
Lovejoy, J.: A Bailey lattice. Proc. Am. Math. Soc. 132, 1507–1516 (2004)
Rowell, M.J.: A new general conjugate Bailey pair. Pac. J. Math. 238, 367–385 (2008)
Schilling, A., Warnaar, S.O.: Conjugate Bailey pairs: from configuration sums and fractional-level string functions to Bailey’s lemma. In: Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory (Charlottesville, VA, 2000). Contemp. Math., vol. 297, pp. 227–255. Amer. Math. Soc, Providence (2002)
Singh, U.B.: A note on a transformation of Bailey. Q. J. Math. Oxf. Ser. (2) 45, 111–116 (1994)
Slater, L.J.: A new proof of Rogers’s transformations of infinite series. Proc. Lond. Math. Soc. 53, 460–475 (1951)
Warnaar, S.O.: Partial theta functions. I. Beyond the lost notebook. Proc. Lond. Math. Soc. 87, 363–395 (2003)
Zagier, D.: Ramanujan’s mock theta functions and their applications. Astérisque 326, 143–164 (2009)
Zwegers, S.: Mock theta functions. PhD Thesis, Utrecht University (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lovejoy, J. Ramanujan-type partial theta identities and conjugate Bailey pairs. Ramanujan J 29, 51–67 (2012). https://doi.org/10.1007/s11139-011-9356-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-011-9356-4