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Second Order Mock Theta Functions

Published online by Cambridge University Press:  20 November 2018

Richard J. McIntosh
Richard J. McIntosh*
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2 e-mail: mcintosh@math.uregina.ca
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Abstract

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In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$, where $\left| q \right|<1$. He called them mock theta functions, because as $q$ radially approaches any point ${{e}^{2\pi ir}}\left( r\,\text{rational} \right)$, there is a theta function ${{F}_{r}}\left( q \right)$ with $F\left( q \right)-{{F}_{r}}\left( q \right)=O\left( 1 \right)$. In this paper we establish the relationship between two families of mock theta functions.

Keywords

11B6533D15q-seriesmock theta functionMordell integral
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 2 , 01 June 2007 , pp. 284 - 290
Copyright
Copyright © Canadian Mathematical Society 2007

References

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