On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials

Erik Koelink, René F. Swarttouw

For the Bessel function \begin{equation} \label{bessel} J_ν(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{ν+2k}}{k! Γ(ν+1+k)} \end{equation} there exist…