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

 

Integral representation for Neumann series of Bessel functions


Authors: Tibor K. Pogány and Endre Süli
Journal: Proc. Amer. Math. Soc. 137 (2009), 2363-2368
MSC (2000): Primary 33C10, 33C20; Secondary 40A05, 44A20
Published electronically: January 22, 2009
MathSciNet review: 2495270
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Abstract: A closed integral expression is derived for Neumann series of Bessel functions -- a series of Bessel functions of increasing order -- over the set of real numbers.


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Additional Information

Tibor K. Pogány
Affiliation: Faculty of Maritime Studies, University of Rijeka, Studentska 2, HR-51000 Rijeka, Croatia
Email: poganj@brod.pfri.hr

Endre Süli
Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, England
Email: Endre.Suli@comlab.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09796-2
PII: S 0002-9939(09)09796-2
Keywords: Bessel function of the first kind $J_\nu (x)$, integral representation of series, Neumann series of Bessel functions
Received by editor(s): May 31, 2007
Received by editor(s) in revised form: September 22, 2008
Published electronically: January 22, 2009
Additional Notes: The first author was supported in part by Research Project No. 112-2352818-2814 of the Ministry of Sciences, Education and Sports of Croatia.
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2009 American Mathematical Society