### Abstract

We derive a closed formula for the determinant of the Hankel matrix whose entries are given by sums of negative powers of the zeros of the regular Coulomb wave function. This new identity applied together with results of Grommer and Chebotarev allows us to prove a Hurwitz-type theorem about the zeros of the regular Coulomb wave function. As a particular case, we obtain a new proof of the classical Hurwitz's theorem from the theory of Bessel functions that is based on algebraic arguments. In addition, several Hankel determinants with entries given by the Rayleigh function and Bernoulli numbers are also evaluated.

Original language | English |
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Pages (from-to) | 259-272 |

Number of pages | 14 |

Journal | Linear Algebra and Its Applications |

Volume | 548 |

DOIs | |

Publication status | Published - Jul 1 2018 |

### Keywords

- Bessel function
- Coulomb wave function
- Hankel determinant
- Rayleigh function

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Baricz, Á., & Štampach, F. (2018). The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants.

*Linear Algebra and Its Applications*,*548*, 259-272. https://doi.org/10.1016/j.laa.2018.03.012