A Riemann-Hilbert Approach to the Heun Equation

Published 7 Sep 2018 in math.CA, math-ph, math.MP, and nlin.SI | (1809.02311v1)

Abstract: We describe the close connection between the linear system for the sixth Painlev\'e 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.

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