Results 1 to 10 of about 7,066 (206)
Entropy, 2021 We derive exactly solvable potentials from the formal solutions of the confluent Heun equation and determine conditions under which the potentials possess PT symmetry.
Géza Lévai
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New solutions of Heun general equation [PDF]
Journal of Physics A: Mathematical and General, 2009 We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation.
Appell P +12 more
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On polynomial solutions of Heun equation [PDF]
Journal of Physics A: Mathematical and General, 2004 By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation.
Bhaduri R K +10 more
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On $q$-deformations of the Heun equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 The $q$-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular we characterize the variants of the $q$-Heun equation by using analysis
Takemura, Kouichi
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Advances in High Energy Physics, 2018 We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before.
T. A. Ishkhanyan +2 more
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Solving Heun's equation using conformal blocks
Nuclear Physics B, 2019 It is known that the classical limit of the second order BPZ null vector decoupling equation for the simplest two 5-point degenerate spherical conformal blocks yields: (i) the normal form of the Heun equation with the complex accessory parameter ...
Marcin Pia̧tek, Artur R. Pietrykowski
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Polynomial Solutions of the Heun Equation
Acta Polytechnica, 2011 We review properties of certain types of polynomial solutions of the Heun equation. Two aspects are particularly concerned, the interlacing property of spectral and Stieltjes polynomials in the case of real roots of these polynomials and asymptotic root ...
B. Shapiro, M. Tater
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From Heun Class Equations to Painlevé Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its confluent cases. The second part of our paper is devoted to Painlevé I-VI equations. Our philosophy is to treat these families of equations in a unified way.
Dereziński, Jan +2 more
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Chiral symmetry and Heun’s equation [PDF]
International Journal of Modern Physics A, 2020 We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun’s equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher-order singularity which requests higher regularity condition demanding that parameters ...
Yoon-Seok Choun, Sang-Jin Sin
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Exact solution of rigid planar rotor in external electric field
Results in Physics, 2022 In this paper we propose a new method for accurately solving the energy levels and analytical wave functions of a rigid planar rotor in an electric field.
Chang-Yuan Chen +6 more
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