Solutions of the bi-confluent Heun equation in terms of the Hermite functions

DOI10.1016/j.aop.2017.04.015zbMath1373.33009arXiv1608.02245OpenAlexW2501682030MaRDI QIDQ1674441

A. M. Ishkhanyan, T. A. Ishkhanyan

Publication date: 2 November 2017

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

Full work available at URL: https://arxiv.org/abs/1608.02245

zbMATH Keywords

series expansionHermite functionbi-confluent Heun equation

Mathematics Subject Classification ID

Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (15)

Unified supersymmetric transformations for the harmonic oscillator and its rational extension ⋮ Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Solving eigenproblem by duality transform ⋮ A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations ⋮ The Maslov index for composite power-law potentials: the case of the first Exton potential ⋮ Schrödinger potentials solvable in terms of the general Heun functions ⋮ Second harmonic Hamiltonian: algebraic and Schrödinger approaches ⋮ Orthogonal polynomials, bi-confluent Heun equations and semi-classical weights ⋮ On properties of a deformed Freud weight ⋮ Exact solutions of the sextic oscillator from the bi-confluent Heun equation ⋮ The second Exton potential for the Schrödinger equation ⋮ A new approach to solve the Schrodinger equation with an anharmonic sextic potential ⋮ Generalized-hypergeometric solutions of the biconfluent Heun equation ⋮ Generalized confluent hypergeometric solutions of the Heun confluent equation ⋮ SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

Uses Software

• DLMF

Cites Work

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