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Journal of the London Mathematical Society 2000 62(2):321-335; doi:10.1112/S0024610700008735
© 2000 by London Mathematical Society
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© The London Mathematical Society

Some Eighth Order Mock Theta Functions

Basil Gordon and Richard J. Mcintosh

Department of Mathematics, University of California Los Angeles, CA 90024, USA, bg{at}sonia.math.ucla.edu
Department of Mathematics and Statistics, University of Regina Regina, Canada S4S 0A2, mcintosh{at}math.uregina.ca

Received 24 September 1997. Revision received 12 January 1999.

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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