On reality and asymptotics of zeros of q-Hankel transforms
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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 Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q(0,1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.
- Mathematics, Statistics & Physics [114 items ]