SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

DOI10.11948/2019.118zbMath1464.33008arXiv1412.0654OpenAlexW3102776262MaRDI QIDQ5859353

A. M. Ishkhanyan

Publication date: 16 April 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0654

zbMATH Keywords

special functionsseries expansionsconfluent Heun equationsmulti-term recurrence relations

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Other functions coming from differential, difference and integral equations (33E30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (3)

A new class of approximate analytical solutions of the Pridmore-Brown equation ⋮ A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations ⋮ Generalized-hypergeometric solutions of the biconfluent Heun equation

Uses Software

• DLMF

Cites Work

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• Schrödinger potentials solvable in terms of the confluent Heun functions
• Relations between linear equations and Painlevé's equations
• Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients
• Heun functions and some of their applications in physics
• Solutions of the bi-confluent Heun equation in terms of the Hermite functions
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Die Lösung der Fuchsschen Differentialgleichung zweiter Ordnung durch hypergeometrische Polynome
• Generalized spheroidal wave equation and limiting cases
• A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole
• Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics
• On the Global Representation of the Solutions of Second-Order Linear Differential Equations Having an Irregular Singularity of Rank One in $\infty $ by Series in Terms of Confluent Hypergeometric Functions
• Hypergeometric Expansions of Heun Polynomials
• Die Lösung der linearen Differentialgleichung 2. Ordnung um zwei einfache Singularitäten durch Reihen nach hypergeometrischen Funktionen.
• On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole
• Solutions for the general, confluent and biconfluent Heun equations and their connection with Abel equations
• Removing false singular points as a method of solving ordinary differential equations
• Confluent Heun equations: convergence of solutions in series of coulomb wavefunctions
• Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• The Klein–Gordon–Fock equation in the curved spacetime of the Kerr–Newman (anti) de Sitter black hole
• Incomplete beta-function expansions of the solutions to the confluent Heun equation
• Solutions for confluent and double-confluent Heun equations
• Nonlinear elastic polymers in random flow
• CERTAIN EXPANSIONS OF SOLUTIONS OF THE HEUN EQUATION
• The Fuchsian equation of second order with four singularities

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