Definition:qCosKLS

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The LaTeX DLMF and DRMF macro \qCosKLS represents a ${\displaystyle{\displaystyle q}}$-analogue of the ${\displaystyle{\displaystyle\cos}}$ function: ${\displaystyle{\displaystyle\mathrm{Cos}_{q}}}$.

This macro is in the category of polynomials.

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

\qCosKLS{q} produces ${\displaystyle{\displaystyle{\displaystyle\mathrm{Cos}_{q}}}}$

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

\qCosKLS{q}@@{z} produces ${\displaystyle{\displaystyle{\displaystyle\mathrm{Cos}_{q}z}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\mathrm{Cos}_{q}\!\left(z\right):=\frac{\mathrm{E}_{q}\!\left(\mathrm{i}z\right)+\mathrm{E}_{q}\!\left(-\mathrm{i}z\right)}{2}=\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binomial{2n}{2}}z^{2n}}{\left(q;q\right)_{2n}}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{Cos}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the ${\displaystyle{\displaystyle{\displaystyle\cos}}}$ function used in KLS: ${\displaystyle{\displaystyle{\displaystyle\mathrm{Cos}_{q}}}}$ : http://drmf.wmflabs.org/wiki/Definition:qCosKLS
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle\mathrm{E}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the ${\displaystyle{\displaystyle{\displaystyle\exp}}}$ function used in KLS: ${\displaystyle{\displaystyle{\displaystyle\mathrm{E}_{q}}}}$ : http://drmf.wmflabs.org/wiki/Definition:qExpKLS
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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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