On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials
Classical Analysis and ODEs
2016-09-07 v1
Abstract
For the Bessel function \begin{equation} \label{bessel} J_{\nu}(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{\nu+2k}}{k! \Gamma(\nu+1+k)} \end{equation} there exist several -analogues. The oldest -analogues of the Bessel function were introduced by F. H. Jackson at the beginning of this century, see M. E. H. Ismail \cite{Is1} for the appropriate references. Another -analogue of the Bessel function has been introduced by W. Hahn in a special case and by H. Exton in full generality, see R. F. Swarttouw \cite{Sw1} for a historic overview. Here we concentrate on properties of the Hahn-Exton -Bessel function and in particular on its zeros and the associated -Lommel polynomials.
Keywords
Cite
@article{arxiv.math/9703215,
title = {On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials},
author = {Erik Koelink and René F. Swarttouw},
journal= {arXiv preprint arXiv:math/9703215},
year = {2016}
}