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 $q$-series, $q$-exponentials

MSC Classifications:

33D05, 11A55, 11K70 show english descriptions $q$-gamma functions, $q$-beta functions and integrals
Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
Harmonic analysis and almost periodicity 33D05 - $q$-gamma functions, $q$-beta functions and integrals
11A55 - Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]
11K70 - Harmonic analysis and almost periodicity

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