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The Hurwitz-type theorem for the regular Coulomb wave function via Hankel determinants
Stockholm University, Faculty of Science, Department of Mathematics. Czech Technical University in Prague, Czech Republic.
Number of Authors: 22018 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 548, p. 259-272Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2018. Vol. 548, p. 259-272
Keywords [en]
Hankel determinant, Coulomb wave function, Bessel function, Rayleigh function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-156773DOI: 10.1016/j.laa.2018.03.012ISI: 000430902300014OAI: oai:DiVA.org:su-156773DiVA, id: diva2:1213212
Available from: 2018-06-04 Created: 2018-06-04 Last updated: 2018-06-04Bibliographically approved

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