Results 171 to 180 of about 7,066 (206)

Heun’s Equation and the Hypergeometric Equation

SIAM Journal on Mathematical Analysis, 1979
The present investigation determines under which circumstances Heun’s equation can be derived from the hypergeometric equation by rational substitutions.
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New Solutions of Heun's Equation

Southeast Asian Bulletin of Mathematics, 2000
The author uses Laplace transform methods to obtain solutions to Heun's equation that are substantially simpler in form than the perturbation type solutions which he had obtained previously [H. Exton, Bull. Soc. Math. Belg., Sér. B, No. 1, 45, 49-57 (1993; Zbl 0786.33009)].
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Spin field equations and Heun’s equations

Astrophysics and Space Science, 2015
The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino (s=1/2), electromagnetic (s=1), Rarita-Schwinger (s=3/2), and gravitational (s=2) fields propagating on this ...
Min Jiang, Xuejing Wang, Zhongheng Li
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The Heun Equation and the Darboux Transformation

Mathematical Notes, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sirota, Yu. N., Smirnov, A. O.
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Heun's equation with nearby singularities

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1999
In this paper, the following Fuchsian equation with four singularities is studied: \[ L_z[y(z)]= p_0(z) y''(z)+ p_1(z) y'(z)+ p_2(z) y(z)= \lambda y(z),\tag{1} \] with \(p_0(z)= z(z- 1)(z+ s)\), \(p_1(z)= c(z- 1)(z+ s)+ dz(z+ s)+ ez(z- 1)\), \(p_2(z)= abz\) and the parameters \(a\), \(b\), \(c\), \(d\), \(e\) satisfy the Fuchs identity \(a+ b+ 1- c- d-
Lay, Wolfgang, Slavyanov, Sergei Yu.
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Heun’s Differential Equations

1995
Abstract Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propagation, electrostatic oscillation, and Schrodinger's equation.
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Symmetries of the Confluent Heun Equation

Journal of Mathematical Sciences, 2003
Here, a group of symmetries of the confluent Heun equation (CHE) is studied. The existence of elementary and integral symmetries leads to some symmetries of the connection matrix, which describes relations among solutions determined at different regular singular points. The integral relations are considered in the form of contour integrals which allows
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Heun’s differential equation

2010
The solutions to the hypergeometric differential equation ― two regular singular points in the finite complex plane (at z = 0 and z = 1) and a regular singular point at infinity ― were analyzed in detail in Chapter 5. In this chapter, the solutions of the differential equation with four regular singular points are investigated. We restrict ourselves to
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Factorization of some confluent Heun’s differential equations

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hounkonnou, Mahouton Norbert, Ronveaux, André, Sodoga, Komi   +2 more
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ASYMPTOTICS OF THE SPECTRUM OF HEUN'S EQUATION AND OF HEUN'S FUNCTIONS

Mathematics of the USSR-Izvestiya, 1992
See the review in Zbl 0742.34004.
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