### 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_{ν}. 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_{ν} and for Bessel functions of the second kind Y_{ν}, K_{ν}, and to give links for the same question for the Hankel functions H ^{ν}_{(1)}, H^{ν}_{(2)}.

Original language | English |
---|---|

Pages (from-to) | 951-960 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### 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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

_{ν}, Y

_{ν}and K

_{ν}.

*Proceedings of the American Mathematical Society*,

*140*(3), 951-960. https://doi.org/10.1090/S0002-9939-2011-11402-3

**Integral representations for Neumann-type series of Bessel functions I _{ν}, Y_{ν} and K_{ν}.** / Baricz, A.; Jankov, Dragana; Pogány, Tibor K.

Research output: Contribution to journal › Article

_{ν}, Y

_{ν}and K

_{ν}',

*Proceedings of the American Mathematical Society*, vol. 140, no. 3, pp. 951-960. https://doi.org/10.1090/S0002-9939-2011-11402-3

}

TY - JOUR

T1 - Integral representations for Neumann-type series of Bessel functions Iν, Yν and Kν

AU - Baricz, A.

AU - Jankov, Dragana

AU - Pogány, Tibor K.

PY - 2012

Y1 - 2012

N2 - 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 Jν. In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν, Kν, and to give links for the same question for the Hankel functions H ν(1), Hν(2).

AB - 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 Jν. In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν, Kν, and to give links for the same question for the Hankel functions H ν(1), Hν(2).

KW - Bessel and modified Bessel functions of the first and second kind

KW - Neumann series of Bessel and modified Bessel functions of first and second kind

UR - http://www.scopus.com/inward/record.url?scp=82255194065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=82255194065&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2011-11402-3

DO - 10.1090/S0002-9939-2011-11402-3

M3 - Article

VL - 140

SP - 951

EP - 960

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -