2024/09/25 by Seok-Young Chung, Chung, Seok-Young
Mathematics · #30C15 #33C45 #34C10 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2409.17305
openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper begins by deriving the uniform bounds for the regular Coulomb wave function Fℓ,η and its derivative Fℓ,η'. We then examine detailed zero configurations of Fℓ,η and Fℓ+1,η, extending insights into the earlier work that was restricted to ℓ>-3/2. Our investigation also includes an analysis of the monotonicity of the zeros of Fℓ,η with respect to parameters ℓ and η, respectively. Furthermore, we expand our exploration to associated orthogonal polynomials, as well as the functions involving both Fℓ,η and Fℓ,η'. Finally, we explore the breakdown of the Sturm separation theorem by means of the zeros of associated orthogonal polynomials.