McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Gil, Amparo, Segura, Javier, Temme, Nico M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212345
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions. Amparo Gil, Javier Segura and Nico M. Temme. SIGMA 20 (2024), 075, 9 pages

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...