Perturbative connection formulas for Heun equations

@article{Lisovyy2022PerturbativeCF,
  title={Perturbative connection formulas for Heun equations},
  author={O Lisovyy and A. Naidiuk},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2022},
  volume={55}
}
  • O. LisovyyA. Naidiuk
  • Published 2 August 2022
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
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… 
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