Jackson q-Bessel (2)

The Jackson $q$-Bessel function $J_{\nu}^{(2)}$ is defined by $$J_{\nu}^{(1)}(x;q)=\dfrac{(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \left( \dfrac{x}{2} \right)^{\nu} {}_0\phi_1 \left(;q^{\nu+1};q;\dfrac{qx^2}{4} \right),$$ where $(\xi,q)_{\infty}$ denotes the $q$-Pochhammer symbol and ${}_0\phi_1$ denotes the basic hypergeometric $\phi$.