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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The zeros of certain Lommel functions


Authors: Stamatis Koumandos and Martin Lamprecht
Journal: Proc. Amer. Math. Soc. 140 (2012), 3091-3100
MSC (2010): Primary 33C10, 33B10; Secondary 42A05, 30C15, 26D15
Published electronically: January 4, 2012
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Abstract: Lommel's function $ s_{\mu ,\nu }(z)$ is a particular solution of the differential equation $ z^{2}y'' + zy' + (z^{2}-\nu ^{2})y = z^{\mu +1}$. Here we present estimates and monotonicity properties of the positive zeros of $ s_{\mu -1/2,1/2}(z)$ when $ \mu \in (0,1)$. The positivity of a closely related integral is also considered.


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Additional Information

Stamatis Koumandos
Affiliation: Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus
Email: skoumand@ucy.ac.cy

Martin Lamprecht
Affiliation: Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus
Email: martin@ucy.ac.cy

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11139-6
PII: S 0002-9939(2012)11139-6
Keywords: Special functions, Lommel functions, positive integrals, zeros.
Received by editor(s): October 8, 2010
Received by editor(s) in revised form: March 21, 2011
Published electronically: January 4, 2012
Additional Notes: The research for this paper was supported by the Leventis Foundation (grant No. 3411-21041).
Communicated by: Walter Van Assche
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.