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An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions

Published online by Cambridge University Press:  20 November 2018

René F. Swarttouw
René F. Swarttouw*
Affiliation:
Delft University of Technology, Faculty of Technical Mathematicsand Informatics, Mekelweg 4, 2628 CD Delft, The Netherlands
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Abstract

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In this paper a q-analogue of Gegenbauer's addition formula for Bessel functions is obtained by using the orthogonality relation for the q-Ultraspherical polynomials of Rogers'. Also some product formulas and an integral representation for the Hahn-Exton q-Bessel functions are obtained.

Keywords

33D1533D45Hahn-Exton q-Bessel functionGegenbauer's addition formulaq-Ultraspherical polynomialsproduct formulasintegral representation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 867 - 879
Copyright
Copyright © Canadian Mathematical Society 1992

References

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