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

A. Baricz, František Štampach

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)259-272
Number of pages14
JournalLinear Algebra and Its Applications
Volume548
DOIs
Publication statusPublished - Jul 1 2018

Fingerprint

Hankel Determinant
Wave functions
Wave Function
Bessel functions
Hankel Matrix
Bernoulli numbers
Zero
Bessel Functions
Theorem
Rayleigh
Determinant
Closed

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

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

In: Linear Algebra and Its Applications, Vol. 548, 01.07.2018, p. 259-272.

Research output: Contribution to journalArticle

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