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SOME EIGHTH ORDER MOCK THETA FUNCTIONS

Published online by Cambridge University Press:  09 January 2001

BASIL GORDON  and
RICHARD J. McINTOSH
BASIL GORDON
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024, USA; [email protected]
RICHARD J. McINTOSH
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Canada S4S 0A2; [email protected]
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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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 321 - 335
Copyright
The London Mathematical Society 2000

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