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Search: All articles in the CMB digital archive with keyword $q$-series

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1. CMB 2007 (vol 50 pp. 284)

McIntosh, Richard J.
Second Order Mock Theta Functions
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
Categories:11B65, 33D15

2. CMB 2005 (vol 48 pp. 147)

Väänänen, Keijo; Zudilin, Wadim
Baker-Type Estimates for Linear Forms in the Values of $q$-Series
We obtain lower estimates for the absolute values of linear forms of the values of generalized Heine series at non-zero points of an imaginary quadratic field~$\II$, in particular of the values of $q$-exponential function. These estimates depend on the individual coefficients, not only on the maximum of their absolute values. The proof uses a variant of classical Siegel's method applied to a system of functional Poincar\'e-type equations and the connection between the solutions of these functional equations and the generalized Heine series.

Keywords:measure of linear independence, $q$-series
Categories:11J82, 33D15

3. CMB 1998 (vol 41 pp. 86)

Lubinsky, D. S.
On \lowercase{$q$}-exponential functions for \lowercase{$|q| =1$}
We discuss the $q$-exponential functions $e_q$, $E_q$ for $q$ on the unit circle, especially their continuity in $q$, and analogues of the limit relation $ \lim_{q\rightarrow 1}e_q((1-q)z)=e^z$.

Keywords:$q$-series, $q$-exponentials
Categories:33D05, 11A55, 11K70

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