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MOCK THETA DOUBLE SUMS

  • JEREMY LOVEJOY (a1) and ROBERT OSBURN (a2) (a3)
Abstract
Abstract

We prove a general result on Bailey pairs and show that two Bailey pairs of Bringmann and Kane are special cases. We also show how to use a change of base formula to pass from the pairs of Bringmann and Kane to pairs used by Andrews in his study of Ramanujan's seventh order mock theta functions. We derive several more Bailey pairs of a similar type and use these to construct a number of new q-hypergeometric double sums which are mock theta functions. Finally, we prove identities between some of these mock theta double sums and classical mock theta functions.

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1. G.E. Andrews , Multiple series Rogers-Ramanujan identities, Pacific J. Math. 114 (1984), 267283.

2. G.E. Andrews , q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, in Regional Conference Series in Mathematics, vol. 66 (American Mathematical Society, Providence, RI, 1986).

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6. G.E. Andrews , Bailey pairs with free parameters, mock theta functions and tubular partitions, Ann. Combin. 18 (2014), 563578.

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10. G. Gasper and M. Rahman , Basic Hypergeometric Series, 2nd edition. Encyclopedia of Mathematics and its Applications, 96 (Cambridge University Press, Cambridge, 2004).

11. B. Gordon and R.J. McIntosh , A survey of classical mock theta functions, in Partitions, q-series, and Modular Forms, Developments in Mathematics, vol. 23 (Springer, New York, 2012), 95144.

12. D. Hickerson and E. Mortenson , Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I, Proc. London Math. Soc. 109 (2014), 382422.

13. J. Lovejoy and R. Osburn , q-hypergeometric double sums as mock theta functions, Pacific J. Math. 264 (2013), no. 1, 151162.

14. J. Lovejoy and R. Osburn , Real quadratic double sums, Indag. Math. 26 (4) (2015), 697712.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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