Definition:JacksonqBesselII

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Definition:JacksonqBesselIII >>

The LaTeX DLMF and DRMF macro \JacksonqBesselII represents the Jackson ${\displaystyle{\displaystyle q}}$-Bessel function 2.

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

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

\JacksonqBesselII{\nu} produces ${\displaystyle{\displaystyle{\displaystyle J^{(2)}_{\nu}}}}$

\JacksonqBesselII{\nu}@{z}{q} produces ${\displaystyle{\displaystyle{\displaystyle J^{(2)}_{\nu}\!\left(z;q\right)}}}$

These are defined by

${\displaystyle{\displaystyle{\displaystyle J^{(2)}_{\nu}\!\left(z;q\right):=\frac{\left(q^{\nu+1};q\right)_{\infty}}{\left(q;q\right)_{\infty}}\left(\frac{z}{2}\right)^{\nu}\,\qHyperrphis{0}{1}@@{-}{q^{\nu+1}}{q}{-\frac{q^{\nu+1}z^{2}}{4}}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle J^{(2)}_{q}}}}$ : Jackson ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel function 2 : http://drmf.wmflabs.org/wiki/Definition:JacksonqBesselII
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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Definition:JacksonqBesselIII >>