Theory and computation of spheroidal wavefunctions

DOI10.1088/0305-4470/36/20/309zbMath1064.33019arXivmath-ph/0212051OpenAlexW3103598160MaRDI QIDQ4450129

Peter E. Falloon, Paul C. Abbott, Jingbo B. Wang

Publication date: 15 February 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0212051

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Computation of special functions and constants, construction of tables (65D20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Lamé, Mathieu, and spheroidal wave functions (33E10) Numerical approximation and evaluation of special functions (33F05) Software, source code, etc. for problems pertaining to special functions (33-04)

Related Items (26)

Integral relations for solutions of the confluent Heun equation ⋮ The performance of local absorbing boundary conditions for acoustic scattering from elliptical shapes ⋮ Influences of prolate spheroidal baffle of sound diffraction on spatial directivity of acoustic vector sensor ⋮ Analytical and numerical investigation of the performance of the BGT2 condition for low-frequency acoustic scattering problems ⋮ Calculation of radial prolate spheroidal wave functions of the second kind ⋮ The nonconvergence of \(h\)-refinement in prolate elements ⋮ Computation of the eigenvalues for the angular and Coulomb spheroidal wave equation ⋮ Calculating the branch points of the eigenvalues of the Coulomb spheroidal wave equation ⋮ Exact solutions to the angular Teukolsky equation with s ≠ 0 ⋮ New Characterizations for the Eigenvalues of the Prolate Spheroidal Wave Equation ⋮ Calculation of the branch points of the eigenfunctions corresponding to wave spheroidal functions ⋮ On the Asymptotic Expansion of the Spheroidal Wave Function and Its Eigenvalues for Complex Size Parameter ⋮ Efficient algorithm for two-center Coulomb and exchange integrals of electronic prolate spheroidal orbitals ⋮ Improvement of the performance of the BGT2 condition for low frequency acoustic scattering problems ⋮ Convergence and applications of some solutions of the confluent Heun equation ⋮ Rényi information from entropic effects in one higher dimension ⋮ Kinematic dynamos in spheroidal geometries ⋮ High-order asymptotics for the spin-weighted spheroidal equation at large real frequency ⋮ Perturbation theory in a framework of iteration methods ⋮ On the numerical evaluation of Fredholm determinants ⋮ Calculation of spheroidal wave functions ⋮ Acoustic scattering by two fluid confocal prolate spheroids ⋮ Exact greybody factors for the brane scalar field of five-dimensional rotating black holes ⋮ The radial action from probe amplitudes to all orders ⋮ A numerical study of the Legendre-Galerkin method for the evaluation of the prolate spheroidal wave functions ⋮ Confluent Heun functions and separation of variables in spheroidal coordinates

Uses Software

• Mathematica

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