Journal of the London Mathematical Society



SOME EIGHTH ORDER MOCK THETA FUNCTIONS


BASIL GORDON a1 and RICHARD J. McINTOSH a2
a1 Department of Mathematics, University of California, Los Angeles, CA 90024, USA; bg@sonia.math.ucla.edu
a2 Department of Mathematics and Statistics, University of Regina, Regina, Canada S4S 0A2; mcintosh@math.uregina.ca

Abstract

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.

(Received September 24 1997)
(Revised January 12 1999)


Dedication:
Dedicated to Tom M. Apostol