Swarttouw, R. F.; Meijer, H. G. A \(q\)-analogue of the Wronskian and a second solution of the Hahn-Exton \(q\)-Bessel difference equation. (English) Zbl 0822.33009 Proc. Am. Math. Soc. 120, No. 3, 855-864 (1994). First the authors define a natural \(q\)-analogue of the Wronskian for two solutions of a general second order linear \(q\)-difference equation. They show that this \(q\)-Wronskian satisfies a first order \(q\)-difference equation, which is a \(q\)-analogue of Abel’s theorem.In the second part of the paper the \(q\)-Wronskian is used to obtain a second solution to the second order \(q\)-difference equation satisfied by the Hahn-Exton \(q\)-Bessel function, which is a \(q\)-analogue of the Bessel function of the first kind \(J_ \nu (x)\). Moreover, it is shown that this second solution is a \(q\)-analogue of the Bessel function of the second kind \(Y_ \nu (x)\). Reviewer: R.Koekoek (Delft) Cited in 9 Documents MSC: 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 33D70 Other basic hypergeometric functions and integrals in several variables Keywords:\(q\)-difference equation; \(q\)-Bessel function; Hahn-Exton PDFBibTeX XMLCite \textit{R. F. Swarttouw} and \textit{H. G. Meijer}, Proc. Am. Math. Soc. 120, No. 3, 855--864 (1994; Zbl 0822.33009) Full Text: DOI