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ON CERTAIN SOLUTIONS FOR CONFLUENT AND DOUBLECONFLUENT HEUN EQUATIONS
, 2008
"... This paper examines some solutions for confluent and doubleconfluent Heun equations. In the first place, we review two Leaver’s solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation and introduce an additional expansion in series of irregular co ..."
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This paper examines some solutions for confluent and doubleconfluent Heun equations. In the first place, we review two Leaver’s solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation and introduce an additional expansion in series of irregular
An algorithm to obtain global solutions of the double confluent Heun equation. Numer. Algorithms
, 2008
"... Abstract. A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wr ..."
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Cited by 1 (0 self)
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Abstract. A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those
1 Integral relations and new solutions to the doubleconfluent Heun equation
, 2004
"... Draft version Integral relations and transformation rules are used to obtain, out of an asymptotic solution, a new group of four pairs of solutions to the doubleconfluent Heun equation. Each pair presents the same series coefficients but has solutions convergent in different regions of the complex ..."
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Draft version Integral relations and transformation rules are used to obtain, out of an asymptotic solution, a new group of four pairs of solutions to the doubleconfluent Heun equation. Each pair presents the same series coefficients but has solutions convergent in different regions of the complex
An example of double confluent Heun equation: Schrödinger equation with supersingular plus Coulomb potential
, 2009
"... A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r −4, plus an attractive Coulombian ..."
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A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r −4, plus an attractive
Confluent Heun Equations: Convergence of Solutions in Series of Coulomb
, 2012
"... The Leaver solutions in series of Coulomb wave functions for the confluent Heun equation are given by twosided infinite series, that is, by series where the summation index n runs from minus to plus infinity [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. First we show that, in contrast to the D’A ..."
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The Leaver solutions in series of Coulomb wave functions for the confluent Heun equation are given by twosided infinite series, that is, by series where the summation index n runs from minus to plus infinity [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. First we show that, in contrast to the D
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Reduction Systems
The modeling of a Josephson junction and Heun polynomials” Preprint Arxiv:mathph/0601064
, 2006
"... Abstract. The first order nonlinear ODE ˙ϕ(t) + sin ϕ(t) = q(t), q(t) = B + Acosωt, where A, B, ω are real constants, is considered, the transformation converting it to a second order linear homogeneous ODE with polynoimial coefficients is found. The latter is identified as a particular case of th ..."
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Cited by 2 (2 self)
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of the double confluent Heun equation. The series of algebraic constraints on the constant parameters is found whose fulfillment leads to the existance of solutions representable through polynomials in explicit form. These polynomials are found to constitute the orthogonal normalizable system. Nowadays
Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations
, 2004
"... In a recent paper, the canonical forms of a new multiparameter class of Abel differential equations, socalled AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a c ..."
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Cited by 8 (0 self)
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connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfluent (BHE) equations is presented. This connection fixes the value of one of the Heun parameters, expresses another one in terms of those remaining, and provides closed form solutions in terms of pFq functions
Results 1  10
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