### Abstract

The goal of present chapter is to study in details the integral representations of the Neumann series (of the first and second type) of Bessel and modified Bessel functions of the first and second kind. In order to achieve our goal we use several methods: the Euler–Maclaurin summation technique, differential equation technique, fractional integration technique. Moreover, we present some interesting results on the coefficients of Neumann series, product of modified Bessel functions of the first and second kind and the cumulative distribution function of the non-central χ^{2}-distribution.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 27-86 |

Number of pages | 60 |

DOIs | |

Publication status | Published - Jan 1 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2207 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Baricz, Á., Jankov Maširević, D., & Pogány, T. K. (2017). Neumann series. In

*Lecture Notes in Mathematics*(pp. 27-86). (Lecture Notes in Mathematics; Vol. 2207). Springer Verlag. https://doi.org/10.1007/978-3-319-74350-9_2