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SIGMA, 2018, Volume 14, 093, 24 pp. (Mi sigma1392)  

A Riemann–Hilbert Approach to the Heun Equation

Boris Dubrovina, Andrei Kapaevb

a SISSA, Via Bonomea 265, 34136, Trieste, Italy
b Deceased

Abstract: 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.

Keywords: Heun polynomials; Riemann–Hilbert problem; Painlevé equations.

Funding Agency Grant Number
Saint Petersburg State University 11.38.215.2014
Acknowledgments A.K. was supported by the project SPbGU 11.38.215.2014.


DOI: https://doi.org/10.3842/SIGMA.2018.093

Full text: PDF file (570 kB)
Full text: https://www.imath.kiev.ua/~sigma/2018/093/
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Bibliographic databases:

MSC: 34M03; 34M05; 34M35; 34M55; 57M50
Received: February 7, 2018; in final form August 15, 2018; Published online September 7, 2018
Language:

Citation: Boris Dubrovin, Andrei Kapaev, “A Riemann–Hilbert Approach to the Heun Equation”, SIGMA, 14 (2018), 093, 24 pp.

Citation in format AMSBIB
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\by Boris~Dubrovin, Andrei~Kapaev
\paper A Riemann--Hilbert Approach to the Heun Equation
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\yr 2018
\vol 14
\papernumber 093
\totalpages 24
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\crossref{https://doi.org/10.3842/SIGMA.2018.093}
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