Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions

Abstract

We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions in general obey three-term recurrence relations defining double-sided infinite series; however, four-term and two-term relations are also possible in particular cases. The conditions for left- and/or right-side termination of the derived series are discussed.

References in corpus (2)

• New solutions of Heun general equation
• Incomplete beta-function expansions of the solutions to the confluent Heun equation

Cited by in corpus (21)

• Solutions of the bi-confluent Heun equation in terms of the Hermite functions
• Schrödinger potentials solvable in terms of the general Heun functions
• Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
• Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function
• Discretization of Natanzon potentials
• Instability of the charged massive scalar field on the Kerr-Newman black hole spacetime
• The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole
• Analytic solutions of the quantum two-state problem in terms of the double-, bi- and tri-confluent Heun functions
• Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence
• The third exactly solvable hypergeometric quantum-mechanical potential
• Exactly solvable Schrödinger equation with double-well potential for hydrogen bond
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
• A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
• Analytical and numerical treatment of perturbed black holes in horizon-penetrating coordinates
• Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
• On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole
• Series solutions of confluent Heun equations in terms of incomplete Gamma-functions
• Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions