Neumann series of Bessel functions

Abstract

Recently, Pogány and Süli [Integral representation for Neumann series of Bessel functions, Proc. Amer. Math. Soc. 137(7) (2009), pp. 2363–2368] derived a closed-form integral expression for a Neumann series of Bessel functions. In this note, our aim is to establish another kind of integral representations for the Neumann series of Bessel functions of the first kind J _ν.

Keywords:

• Neumann series
• Bessel functions
• integral representation

2000 Mathematics Subject Classifications::

• Primary: 40H05, 40A30
• Secondary: 33C10

Acknowledgements

The work of the first 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_388/2011.