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Euler Integral Symmetries and the Asymptotics of the Monodromy for the Heun Equation
Euler integral transform connects monodromy matrices of the Heun equation with different sets of parameters. In this paper, this fact is used to...
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Solutions of a Confluent Modification of the General Heun Equation in Terms of Generalized Hypergeometric Functions
AbstractWe consider a confluent modification of the general Heun equation having three regular singular points and an irregular singularity of rank...
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The Harmonic Lagrange Top and the Confluent Heun Equation
The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global...
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Generalized-hypergeometric solutions of the biconfluent Heun equation
Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear...
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Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation
A family of quadruplets of interrelated functions holomorphic on the universal cover of the complex plane without zero (for brevity,
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Stokes Matrices of a Reducible Double Confluent Heun Equation via Monodromy Matrices of a Reducible General Huen Equation with Symmetric Finite Singularities
We study the effect of the unfolding of a reducible double confluent Heun equation from the point of view of the Stokes phenomenon. We introduce a...
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Functional equations related to Appell polynomials and Heun functions
We are concerned with a functional equation related to equations satisfied by Legendre and Laguerre polynomials. Its solutions are expressed in terms...
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Exact Solutions of the Schrödinger Equation for a Radial Generalized Cornell Plus an Extended Double Ring-Shaped Potential
In this work, we solve the Schrödinger equation for the generalized Cornell potential plus an extended ring-shaped potential in the framework of...
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The rational Heun operator and Wilson biorthogonal functions
We consider the rational Heun operator defined as the most general second-order q -difference operator which sends any rational function of type
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First-Order Ode Systems Generating Confluent Heun Equations
We study the relation between linear second-order equations that are confluent Heun equations, namely, the biconfluent and triconfluent Heun...
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Elementary hypergeometric functions, Heun functions, and moments of MKZ operators
We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-König and...
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On the Derivatives of the Heun Functions
AbstractThe Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first...
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An Explanation of the Commuting Operator “Miracle” in Time and Band Limiting
Time and band limiting operators are expressed as functions of the confluent Heun operator arising in the spheroidal wave equation. Explicit formulas...
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Signal Processing, Orthogonal Polynomials, and Heun Equations
A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal...
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Heterogeneous Multiscale Methods for the Landau–Lifshitz Equation
In this paper, we present a finite difference Heterogeneous Multiscale Method for the Landau–Lifshitz equation with a highly oscillatory diffusion...
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Liouvillian solutions for second order linear differential equations with Laurent polynomial coefficient
This paper is devoted to a complete parametric study of Liouvillian solutions of the general trace-free second order differential equation with a...
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The boundary value problem for the mean field equation on a compact Riemann surface
Let (Σ, g ) be a compact Riemann surface with smooth boundary ∂E, ∆ g be the Laplace-Beltrami operator, and h be a positive smooth function. Using a...
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Movable singularity of semi linear Heun equation and application to blowup phenomenon
In this paper we shall study the movable singularity of semi linear Heun equation and its application to the blowup of a semi linear wave equation....