We study the relation between linear second-order equations that are confluent Heun equations, namely, the biconfluent and triconfluent Heun equations, and first-order linear systems of equations generating Painlevé equations. The generation process is interpreted in physical terms as antiquantization. Technically, the study in volves manipulations with polynomials. The complexity of computations sometimes requires using computer algebra systems. Bibliography: 13 titles.
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S.Yu. Slavyanov is deceased
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 485, 2019, pp. 187–194.
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Salatich, A.A., Slavyanov, S. & Stesik, O.L. First-Order Ode Systems Generating Confluent Heun Equations. J Math Sci 251, 427–432 (2020). https://doi.org/10.1007/s10958-020-05102-7
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DOI: https://doi.org/10.1007/s10958-020-05102-7