Hahn-Exton q-Bessel
From specialfunctionswiki
The Hahn-Exton $q$-Bessel function, also called the Jackson $q$-Bessel function $J_{\nu}^{(3)}$, is defined by $$J_{\nu}^{(3)}(x;q)=\dfrac{x^{\nu}(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \displaystyle\sum_{k \geq 0}\dfrac{(-1)^kq^{\frac{k(k+1)}{2}}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k}.$$
