Definition:qexpKLS

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The LaTeX DLMF and DRMF macro \qexpKLS represents a ${\displaystyle{\displaystyle q}}$-analogue of the ${\displaystyle{\displaystyle\exp}}$ function: ${\displaystyle{\displaystyle\mathrm{e}_{q}}}$.

This macro is in the category of real or complex valued functions.

In math mode, this macro can be called in the following ways:

\qexpKLS{q} produces ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}}}}$

\qexpKLS{q}@{z} produces ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}\!\left(z\right)}}}$

\qexpKLS{q}@@{z} produces ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}z}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}\!\left(z\right):=\qHyperrphis{1}{0}@@{0}{-}{q}{z}:=\sum_{n=0}^{\infty}\frac{z^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left(z;q\right)_{\infty}},\quad 0<|q|<1}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the ${\displaystyle{\displaystyle{\displaystyle\exp}}}$ function used in KLS: ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}}}}$ : http://drmf.wmflabs.org/wiki/Definition:qexpKLS
${\displaystyle{\displaystyle{\displaystyle\mathrm{exp}}}}$ : exponential function : http://dlmf.nist.gov/4.2#E19
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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