Results 21 to 30 of about 7,066 (206)
Jacobi elliptic coordinates, functions of Heun and Lame type and the Niven transform [PDF]
, 2005 Lame and Heun functions arise via separation of the Laplace equation in general Jacobi ellipsoidal or conical coordinates. In contrast to hypergeometric functions that also arise via variable separation in the Laplace equation, Lame and Heun functions ...
Kalnins, Ernie G., Miller, W., Jr.
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RELATIONS BETWEEN HEUN EQUATIONS AND PAINLEVE EQUATIONS
Albanian Journal of Mathematics, 2010 Summary: The article is focused on the following items: 1. Relations between Heun equation, the corresponding deformed equation with added apparent singularity and the corresponding \(2\times 2\) systems and \(3\times 3\) systems of first order equations. 2. Integral transforms linking deformed Heun equations. 3.
Kazakov, Alexander Yakov +2 more
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Tridiagonalization and the Heun equation [PDF]
Journal of Mathematical Physics, 2017 It is shown that the tridiagonalization of the hypergeometric operator L yields the generic Heun operator M. The algebra generated by the operators L, M and Z = [L, M] is quadratic and a one-parameter generalization of the Racah algebra. The Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the ...
Grünbaum, F. Alberto +2 more
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European Physical Journal C: Particles and Fields, 2018 We point out a misleading treatment in a recent paper published in this Journal (Sobhani et al., Eur Phys J C 78:106, 2018) regarding solutions for the Schrödinger equation with a anharmonic oscillator potential embedded in the background of a cosmic ...
Francisco A. Cruz Neto, Luis B. Castro
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Heun equations and combinatorial identities
Constructive Mathematical Analysis, 2021 Heun functions are important for many applications in Mathematics, Physics and in thus in interdisciplinary phenomena modelling. They satisfy second order differential equations and are usually represented by power series. Closed forms and simpler polynomial representations are useful.
Adina Barar, Gabriela Mocanu, Ioan Raşa
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Schrödinger Potentials with Polynomial Solutions of Heun-Type Equations
MathematicsThe present review discusses the solution of the Heun, confluent, biconfluent, double confluent, and triconfluent equations in terms of polynomial expansions, and applies the results to generate exactly solvable Schrödinger potentials. Although there are
Géza Lévai, Tibor Soltész
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Exact solutions of the angular Teukolsky equation for particular cases
Results in Physics, 2021 In this work we solve the angular Teukolsky equation in alternative way for a more general case τ≠0 but m=0,s=0. We first transform this equation to a confluent Heun differential equation and then construct the Wronskian determinant to calculate the ...
Chang-Yuan Chen +5 more
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Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions [PDF]
, 2010 We present an analytical treatment of coherent excitation of a Two-Level Atom driven by a far-off resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable.
A. M. Dykhne +15 more
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Elliptic solitons and Heun’s equation [PDF]
, 2002 We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's polynomials is studied.
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Comment on “Comment on Linear confinement of a scalar particle in a Gödel-type space-time”
European Physical Journal C: Particles and Fields, 2020 We show that from an appropriate manipulation of the biconfluent Heun differential equation one can obtain the correct expression for the energy eigenvalues for the Klein–Gordon equation without potential in the background of Som–Raychaudhuri space-time ...
Francisco A. Cruz Neto +2 more
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