2021/03/31 by Yuri Krynytskyi, Andrij Rovenchak
Mathematics · Physics and Astronomy · #Applied mathematics #Combinatorics #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Estimation #Exponential function #Exponential growth #Mathematical analysis #Mathematics #Order (exchange) #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #math-ph #math.MP
paper · pdf · doi:10.3842/sigma.2021.057
published as SIGMA 17 (2021), 057, 7 pages
openalex created_date 2021/03/15 · arxiv created 2021/06/10 · openalex publication_date 2021/06/10 · arxiv updated 2021/06/11 · openalex updated_date 2026/08/05
The paper presents the derivation of the asymptotic behavior of -zeros of the modified Bessel function of imaginary order K i (z). This derivation is based on the quasiclassical treatment of the exponential potential on the positive half axis. The asymptotic expression for the -zeros (zeros with respect to order) contains the Lambert W function, which is readily available in most computer algebra systems and numerical software packages. The use of this function provides much higher accuracy of the estimation comparing to known relations containing the logarithm, which is just the leading term of W (x) at large x. Our result ensures accuracies sufficient for practical applications.