Some Eighth Order Mock Theta Functions

@article{Gordon2000SomeEO,
  title={Some Eighth Order Mock Theta Functions},
  author={Basil Gordon and Richard J. McIntosh},
  journal={Journal of the London Mathematical Society},
  year={2000},
  volume={62}
}
A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q‐series expansions. The method is then used to construct several new mock theta functions, including the first ones of eighth order. Summation and transformation formulae for basic hypergeometric series are used to prove that the new functions actually have the mock theta property. The modular transformation formulae for these functions are obtained. 
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References

SHOWING 1-10 OF 14 REFERENCES
Some Asymptotic Formulae for q-Hypergeometric Series
We obtain complete asymptotic expansions for certain ^-hypergeometric series, including those pertaining to the Rogers-Ramanujan identities. Comparing asymptotic expansions associated with different
Collected Papers
THIS volume is the first to be produced of the projected nine volumes of the collected papers of the late Prof. H. A. Lorentz. It contains a number of papersnineteen in all, mainly printed
Asymptotic Transformations of q-Series
Abstract For the $q$ -series $\sum\nolimits_{n=0}^{\infty }{{{a}^{n}}{{q}^{b{{n}^{2}}+cn}}/}\,{{(q)}_{n}}$ we construct a companion $q$ -series such that the asymptotic expansions of their logarithms
an account of the mock theta functions ’, J
  • London Math. Soc. 11
  • 1936
Basic hypergeometric series (Cambridge
  • 1990
...
...