Formula:KLS:01.14:17

<< Formula:KLS:01.14:16

formula in Some q-analogues of special functions

Formula:KLS:01.15:01 >>

${\displaystyle{\displaystyle{\displaystyle\lim\limits_{q\rightarrow 1}J^{(3)}_{\nu}\!\left((1-q)z;q\right)=J_{\nu}\left(2z\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle J_{\nu}}}}$ : Bessel function of the first kind : http://dlmf.nist.gov/10.2#E2

Bibliography

Equation in Section 1.14 of KLS.

URL links

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<< Formula:KLS:01.14:16

formula in Some q-analogues of special functions

Formula:KLS:01.15:01 >>