Definition:qExpKLS

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

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 $\displaystyle \qExpKLS{q}$
\qExpKLS{q}@{z} produces $\displaystyle \qExpKLS{q}@{z}$
\qExpKLS{q}@@{z} produces $\displaystyle \qExpKLS{q}@@{z}$

These are defined by $\displaystyle \qExpKLS{q}@{z}:=\qHyperrphis{0}{0}@@{-}{-}{q}{-z}:= \sum_{n=0}^{\infty}\frac{q^{\binom{n}{2}}}{\qPochhammer{q}{q}{n}}z^n=\qPochhammer{-z}{q}{\infty},\quad 0<|q|<1.$

Symbols List

$\mathrm {E} _{q}}$ : $q}$ -analogue of the $\exp }$ function used in KLS: $\mathrm {E} _{q}}$ : http://drmf.wmflabs.org/wiki/Definition:qExpKLS
$\mathrm {exp} }$ : exponential function : http://dlmf.nist.gov/4.2#E19
${{}_{r}\phi _{s}}}$ : basic hypergeometric (or $q}$ -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
$\Sigma }$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\binom {n}{k}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$(a;q)_{n}}$ : $q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1