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 ${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}_{q}\!\left(z\right):=\frac{\mathrm{e}_{q}\!\left(iz)+{\mathrm{e}}_{q}(-iz\right)}{2}=\sum_{n=0}^{\infty}\frac{(-1)^{n}z^{2n}}{\left(q;q\right)_{2n}}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the ${\displaystyle{\displaystyle{\displaystyle\cos}}}$ function used in KLS: ${\displaystyle{\displaystyle{\displaystyle\cos_{q}}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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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