A Riemann-Hilbert Approach to the Heun Equation
Copyright policy )A Riemann-Hilbert Approach to the Heun Equation
We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions and show how, in the case of reducible monodromy, the Riemann-Hilbert formalism can be used to construct explicit polynomial solutions of the Heun equation.
Riemann-Hilbert problem, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Linear ordinary differential equations and systems in the complex domain, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Painlevé equations, Mathematical Physics (math-ph), Mathematics - Classical Analysis and ODEs, Heun equation, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, General geometric structures on low-dimensional manifolds, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Heun polynomials, Heun polynomials; Painlevé equations; Riemann-Hilbert problem; Analysis; Mathematical Physics; Geometry and Topology, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
Riemann-Hilbert problem, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Linear ordinary differential equations and systems in the complex domain, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Painlevé equations, Mathematical Physics (math-ph), Mathematics - Classical Analysis and ODEs, Heun equation, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, General geometric structures on low-dimensional manifolds, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Heun polynomials, Heun polynomials; Painlevé equations; Riemann-Hilbert problem; Analysis; Mathematical Physics; Geometry and Topology, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
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