Definition:qExpKLS

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Definition:qexpKLS >>

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 ${\displaystyle{\displaystyle{\displaystyle\mathrm{E}_{q}\!\left(z\right):=\qHyperrphis{0}{0}@@{-}{-}{q}{-z}:=\sum_{n=0}^{\infty}\frac{q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}}{\left(q;q\right)_{n}}z^{n}=\left(-z;q\right)_{\infty},\quad 0<|q|<1.}}}$

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
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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