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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 075, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.075 (Mi sigma2077) 		 
McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions

Amparo Gila, Javier Seguraa, Nico M. Temmeb

a Universidad de Cantabria, 39005 Santander, Spain
b Valkenierstraat 25, 1825BD Alkmaar, The Netherlands
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DOI: https://doi.org/10.3842/SIGMA.2024.075
Abstract: We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parameter is equal to zero. Numerical tests are provided to demonstrate the accuracy of the expansions.
Keywords: Coulomb wave functions, McMahon-type zeros, asymptotic expansions.
Funding agency Grant number
Ministerio de Ciencia, Innovacin y Universidades Agencia Estatal de Investigacin 2021-127252NB-I00
We acknowledge financial support from Ministerio de Ciencia e Innovación, Spain, project PID2021-127252NB-I00 (MCIN/AEI/10.13039/501100011033/ FEDER, UE).
Received: February 23, 2024; in final form August 7, 2024; Published online August 10, 2024
Document Type: Article
MSC: 33C47, 33C10, 33C15, 41A60, 65D20, 65H05
Language: English
Citation: Amparo Gil, Javier Segura, Nico M. Temme, “McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions”, SIGMA, 20 (2024), 075, 9 pp.
Citation in format AMSBIB
\Bibitem{GilSegTem24}
\by Amparo~Gil, Javier~Segura, Nico~M.~Temme
\paper McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions
\jour SIGMA
\yr 2024
\vol 20
\papernumber 075
\totalpages 9
\mathnet{http://mi.mathnet.ru/sigma2077}
\crossref{https://doi.org/10.3842/SIGMA.2024.075}
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