Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Authors: R. F. Swarttouw and H. G. Meijer
Journal: Proc. Amer. Math. Soc. 120 (1994), 855-864
MSC: Primary 33D15; Secondary 33D45
MathSciNet review: 1180467
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Abstract: A second solution of the $ q$-difference equation of the Hahn-Exton $ q$-Bessel function, corresponding to the classical $ {Y_\nu }(x)$, is found. We introduce a $ q$-extension of the Wronskian to determine that the two solutions form a fundamental set.

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Keywords: Hahn-Exton $ q$-Bessel function, $ q$-Wronskian, $ q$-difference equation
Article copyright: © Copyright 1994 American Mathematical Society