Solving second-order differential equations in terms of confluent Heun's functions

DOI10.1002/MMA.10001MaRDI QIDQ6560072

Shayea Aldossari

Publication date: 21 June 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

transformationschange of variablesgeneralized exponentsHeun's equationexp-productHeun's function

Mathematics Subject Classification ID

Other functions coming from differential, difference and integral equations (33E30) Other special orthogonal polynomials and functions (33C47) Linear ordinary differential equations and systems in the complex domain (34M03)

Cites Work

• Formal solutions and factorization of differential operators with power series coefficients
• Factorization of differential operators with rational functions coefficients
• Generalized confluent hypergeometric solutions of the Heun confluent equation
• Factorization of some confluent Heun's differential equations
• Finding all bessel type solutions for linear differential equations with rational function coefficients
• The quantum Rabi model: solution and dynamics
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Ince’s limits for confluent and double-confluent Heun equations
• Classes of exact solutions to the Teukolsky master equation
• Solutions for the general, confluent and biconfluent Heun equations and their connection with Abel equations
• On Fuchs' relation for linear differential systems
• Confluent Heun equations: convergence of solutions in series of coulomb wavefunctions
• Solving differential equations in terms of bessel functions
• Incomplete beta-function expansions of the solutions to the confluent Heun equation
• Single polymer dynamics in elongational flow and the confluent Heun equation
• Solutions for confluent and double-confluent Heun equations
• Computing pullback function of second order differential operators by using their semi-invariants

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