Formula:KLS:01.14:14

<< Formula:KLS:01.14:13

formula in Some q-analogues of special functions

Formula:KLS:01.14:15 >>

${\displaystyle{\displaystyle{\displaystyle J^{(2)}_{\nu}\!\left(z;q\right)=\left(-\frac{z^{2}}{4};q\right)_{\infty}\cdot J^{(1)}_{\nu}\!\left(z;q\right)}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle|z|<2}}}$

Proof

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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
${\displaystyle{\displaystyle{\displaystyle J^{(1)}_{q}}}}$ : Jackson ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel function 1 : http://drmf.wmflabs.org/wiki/Definition:JacksonqBesselI

Bibliography

Equation in Section 1.14 of KLS.

URL links

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<< Formula:KLS:01.14:13

formula in Some q-analogues of special functions

Formula:KLS:01.14:15 >>