The Hahn-Exton $q$-Bessel function as the characteristic function of a Jacobi matrix

Frantisek Stampach, Pavel Stovicek

A family ${\mathcal{T}}^{(\nu )}$, $\nu \in \mathbb{R}$, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton $q$-difference equation. The co…