A q-analogue of the Wronskian and a second solution of the Hahn-Exton q-Bessel difference equation

: A second solution of the q-difference equation of the Hahn-Exton q-Bessel function, corresponding to the classical Y (x), is found. We introduce a q-extension of the Wronskian to determine that the two solutions form a fundamental set. Key words: Hahn-Exton q-Bessel function, q-Wronskian, q-difference equation. AMS Subject Classification: 33D15, 33D45. 1 Introduction In mathematics very much attention is paid to the subject of differential equations. However, the theory of q-extensions of differential equations has not yet been developed to a great extent. This can partially be explained by the fact that one is not very familiar with q-theory and the fact that basic differential equations do not occur frequently in physics. But the most important fact is probably the close relationship with difference equations instead of differential equations. q-Differential (or q-difference) equations may even properly be regarded as a part of the field of difference equations. Results on di..