Definition:JacksonqBesselIII

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The LaTeX DLMF and DRMF macro \JacksonqBesselIII represents the Jackson ${\displaystyle{\displaystyle q}}$-Bessel function 3.

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

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

\JacksonqBesselIII{\nu} produces ${\displaystyle{\displaystyle{\displaystyle J^{(3)}_{\nu}}}}$

\JacksonqBesselIII{\nu}@{z}{q} produces ${\displaystyle{\displaystyle{\displaystyle J^{(3)}_{\nu}\!\left(z;q\right)}}}$

These are defined by

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a;q\right):=\qHyperrphis{2}{1}@@{q^{-n},0}{aq}{q}{qx}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle J^{(3)}_{q}}}}$ : Jackson/Hahn-Exton ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel function 3 : http://drmf.wmflabs.org/wiki/Definition:JacksonqBesselIII
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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