Formula:KLS:01.14:16

<< Formula:KLS:01.14:15

formula in Some q-analogues of special functions

Formula:KLS:01.14:17 >>

${\displaystyle{\displaystyle{\displaystyle J^{(3)}_{\nu}\!\left(z;q\right):=\frac{\left(q^{\nu+1};q\right)_{\infty}}{\left(q;q\right)_{\infty}}z^{\nu}\,\qHyperrphis{1}{1}@@{0}{q^{\nu+1}}{q}{qz^{2}}}}}$

Proof

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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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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

Bibliography

Equation in Section 1.14 of KLS.

URL links

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<< Formula:KLS:01.14:15

formula in Some q-analogues of special functions

Formula:KLS:01.14:17 >>