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

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- by Árpád Baricz, Dragana Jankov and Tibor K. Pogány PDF
- Proc. Amer. Math. Soc.
**140**(2012), 951-960 Request permission

## 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
- MR Author ID: 729952
- 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
- 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-PD
__388/2010.__ - Communicated by: Sergei K. Suslov
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2869079