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# Second Order Mock Theta Functions

Published:2007-06-01
Printed: Jun 2007
• Richard J. McIntosh
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## Abstract

In his last letter to Hardy, Ramanujan defined 17 functions $F(q)$, where $|q|<1$. He called them mock theta functions, because as $q$ radially approaches any point $e^{2\pi ir}$ ($r$ rational), there is a theta function $F_r(q)$ with $F(q)-F_r(q)=O(1)$. In this paper we establish the relationship between two families of mock theta functions.
 Keywords: $q$-series, mock theta function, Mordell integral
 MSC Classifications: 11B65 - Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30] 33D15 - Basic hypergeometric functions in one variable, ${}_r\phi_s$

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