On reality and asymptotics of zeros of image-Hankel transforms Original Research Article

We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouchéʹs theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on image. We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.