On polynomial solutions of Heun equation
arXiv:math-ph/0410015 · doi:10.1088/0305-4470/37/46/L01
Abstract
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, $- \s/x$, is also amenable for polynomial solutions.
4 pages, No figure
References in corpus (6)
- Perturbations of Kerr-de Sitter Black Hole and Heun's Equations
- The Heun equation and the Calogero-Moser-Sutherland system I: the Bethe Ansatz method
- Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?
- Novel correlations in two dimensions: Two-body problem
- Finite lattice Bethe ansatz systems and the Heun equation
- Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
Cited by in corpus (16)
- Bounding the greybody factors for Schwarzschild black holes
- Heun Functions and Some of Their Applications in Physics
- Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
- Relativistic Killingbeck Energy States Under an External Magnetic Fields
- Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions
- Potentials of the Heun class
- Analytical solutions for a two-level system driven by a class of chirped pulses
- Special functions associated with positive linear operators
- Operational Methods in the Study of Sobolev-Jacobi Polynomials
- Approximative Analytic Study of Fermions in Magnetar's Crust; Ultra-relativistic Plane Waves, Heun and Mathieu Solutions and Beyond
- Combinatorics of chemical reaction systems
- Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution
- Resonant frequencies of the hydrodynamic vortex
- Information Entropy and Correlation of the Hooke's Atom
- On the Applications of a New Technique to Solve Linear Differential Equations, with and without Source
- Heun polynomials and exact solutions for the massless Dirac particle in the C-metric