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A Note on the Orthogonality of Jackson's q-Bessel Functions

Published online by Cambridge University Press:  20 November 2018

Mizan Rahman
Mizan Rahman*
Affiliation:
Dept. of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 Canada
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Abstract

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A q-analogue of the orthogonality property of the Bessel functions on the zeros is obtained in terms of a q-integral.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 369 - 376
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Erdélyi, A., éd., Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, 1953.Google Scholar
2. Exton, H., q-Hypergeometric Functions and Applications, Ellis Horwood Ltd., Chichester, U.K., 1983.Google Scholar
3. Hahn, W., Beitrâge zur théorie der Heineschen Reichen, Math. Nachr. 2 (1949), 340–379.Google Scholar
4. H, M. E.. Ismail, The zeroes of basic Bessel functions, the function Jv+ax and associated orthogonal polynomials, J. Math. Anal. Appl., 86 (1982), 1–19.Google Scholar
5. H, M. E.. Ismail, The basic Bessel functions and polynomials, SIAM J. Math. Anal. 12 (1981), 454–468.Google Scholar
6. Jackson, F. H., On generalized functions of Le gendre and Bessel, Trans. Roy. Soc. Edin. 41 (1903), 1–28.Google Scholar
7. Rahman, Mizan, An integral representation and some transformation properties of q-Bessel functions, J. Math. Anal. Appl. 125 (1987), 58–71.Google Scholar
8. Rahman, Mizan, An addition theorem and some product formulas for q-Bessel functions, Can. J. Math., 40 (1988), 1203–1221.Google Scholar
9. Some infinite integrals of q-B es sel functions, to appearGoogle Scholar