Solutions for confluent and double-confluent Heun equations

DOI10.1063/1.2970150zbMath1152.81421arXiv0807.2219OpenAlexW1968526563MaRDI QIDQ5505026

Bartolomeu D. B. Figueiredo, Léa Jaccoud El-Jaick

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/0807.2219

Mathematics Subject Classification ID

Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (18)

Elementary integral series for Heun functions: Application to black-hole perturbation theory ⋮ Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Heun functions and some of their applications in physics ⋮ Integral relations for solutions of the confluent Heun equation ⋮ Schrödinger potentials solvable in terms of the confluent Heun functions ⋮ The d-dimensional softcore Coulomb potential and the generalized confluent Heun equation ⋮ A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations ⋮ On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole ⋮ Non-unitary evolution in the general extended EFT of inflation \& excited initial states ⋮ Generalized Dirac oscillator in cosmic string space-time ⋮ Convergence and applications of some solutions of the confluent Heun equation ⋮ A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole ⋮ Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities ⋮ Generalized-hypergeometric solutions of the biconfluent Heun equation ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions ⋮ Generalized confluent hypergeometric solutions of the Heun confluent equation ⋮ Analytical solutions for fermions on a thick brane with a piecewise and smooth warp factor ⋮ SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators
• Quasi-exactly-solvable problems and sl(2) algebra
• Ince’s limits for confluent and double-confluent Heun equations
• Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries
• Generalized spheroidal wave equation and limiting cases
• Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics
• On some solutions to generalized spheroidal wave equations and applications
• Schrödinger equation with inverse fourth-power potential, a differential equation with two irregular singular points
• A novel quasi-exactly solvable model with total transmission modes

This page was built for publication: Solutions for confluent and double-confluent Heun equations