A Riemann-Hilbert Approach to the Heun Equation

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.

References in corpus (7)

• Heun Functions and Some of Their Applications in Physics
• Classical Conformal Blocks and Painleve VI
• The 192 Solutions of the Heun Equation
• Rational Solutions of the Painleve' VI Equation
• Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)
• Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)
• Integral transformation of Heun's equation and some applications

Cited by in corpus (6)

• Confluent conformal blocks and the Teukolsky master equation
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Quantum spectral problems and isomonodromic deformations
• Elementary Integral Series for Heun Functions. With an Application to Black-Hole Perturbation Theory
• q-Heun equation and initial-value space of q-Painlevé equation
• Isomonodromy sets of accessory parameters for Heun class equations