Generalized hypergeometric solutions of the Heun equation
arXiv:1802.04263 · doi:10.1134/S0040577920010018
Abstract
We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters: a characteristic exponent of one of the singularities should be a non-zero integer, and the accessory parameter must satisfy a polynomial equation.
References in corpus (12)
- Heun Functions and Some of Their Applications in Physics
- On reducing the Heun equation to the hypergeometric equation
- Schrödinger potentials solvable in terms of the general Heun functions
- Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations
- Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
- The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole
- Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
- Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
- The third exactly solvable hypergeometric quantum-mechanical potential
- Time-reversal focusing of an expanding soliton gas in disordered replicas
- Parametric transformations between the Heun and Gauss hypergeometric functions
- Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients