### 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 |
---|---|

Pages (from-to) | 259-272 |

Number of pages | 14 |

Journal | Linear Algebra and Its Applications |

Volume | 548 |

DOIs | |

Publication status | Published - Jul 1 2018 |

### Fingerprint

### 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

### Cite this

*Linear Algebra and Its Applications*,

*548*, 259-272. https://doi.org/10.1016/j.laa.2018.03.012

**The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants.** / Baricz, A.; Štampach, František.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants

AU - Baricz, A.

AU - Štampach, František

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - Bessel function

KW - Coulomb wave function

KW - Hankel determinant

KW - Rayleigh function

UR - http://www.scopus.com/inward/record.url?scp=85043515663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043515663&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.03.012

DO - 10.1016/j.laa.2018.03.012

M3 - Article

AN - SCOPUS:85043515663

VL - 548

SP - 259

EP - 272

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -