Perturbative connection formulas for Heun equations

Abstract

Connection formulas relating Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed in terms of the large order asymptotics of the corresponding power series. We demonstrate that for the usual, confluent and reduced confluent Heun equation, the series expansion of the relevant asymptotic amplitude in a suitable parameter can be systematically computed to arbitrary order. This allows to check a recent conjecture of Bonelli-Iossa-Panea Lichtig-Tanzini expressing the Heun connection matrix in terms of quasiclassical Virasoro conformal blocks.

arXiv comment17 pages, 2 figures; v2: added refs

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• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
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• Painlevé Kernels and Surface Defects at Strong Coupling
• Ergodic Hysteresis of the Kerr black hole spectrum