Geodesic
A Riemann–Hilbert Approach to the Heun Equation
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Heun polynomials; Riemann–Hilbert problem; Painlevé equations. 
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     author = {Boris Dubrovin and Andrei Kapaev},
     title = {A {Riemann{\textendash}Hilbert} {Approach} to the {Heun} {Equation}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a92/}
}
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Boris Dubrovin; Andrei Kapaev. A Riemann–Hilbert Approach to the Heun Equation. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a92/

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