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Integral representations for Neumann-type series of Bessel functions $ I_\nu,$ $ Y_\nu$ and $ K_\nu$


Authors: Árpád Baricz, Dragana Jankov and Tibor K. Pogány
Journal: Proc. Amer. Math. Soc. 140 (2012), 951-960
MSC (2010): Primary 40H05, 40A30; Secondary 33C10
DOI: https://doi.org/10.1090/S0002-9939-2011-11402-3
Published electronically: October 5, 2011
MathSciNet review: 2869079
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Abstract: Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363-2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind $ J_\nu $. In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind $ I_\nu $ and for Bessel functions of the second kind $ Y_\nu , K_\nu $, and to give links for the same question for the Hankel functions $ H_\nu ^{(1)}, H_\nu ^{(2)}$.


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Additional Information

Árpád Baricz
Affiliation: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
Email: bariczocsi@yahoo.com

Dragana Jankov
Affiliation: Department of Mathematics, University of Osijek, 31000 Osijek, Croatia
Email: djankov@mathos.hr

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

DOI: https://doi.org/10.1090/S0002-9939-2011-11402-3
Keywords: Bessel and modified Bessel functions of the first and second kind, Neumann series of Bessel and modified Bessel functions of first and second kind
Received by editor(s): December 17, 2010
Published electronically: October 5, 2011
Additional Notes: The research of the first-named author was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the Romanian National Authority for Scientific Research CNCSIS-UEFISCSU, project number PN-II-RU-PD388/2010.
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2011 American Mathematical Society

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