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}
}
• Published 1 October 2000
• Mathematics
• Journal of the London Mathematical Society
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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