Geodesic
Systems of first order ODE generating confluent Heun equations
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 187-194

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Relation between linear second order equations being confluent Heun equations: biconfluent and triconfluent – and first order linear systems of equations which generate Painlevë equations is studied. The generation process is interpreted in physical terms as antiquantization.Technically the study includes manipulations with polynomials. The complexity of computations sometimes demands the use of Algebraic Computing Systems. 
@article{ZNSL_2019_485_a10,
     author = {A. A. Salatich and S. Yu. Slavyanov and O. L. Stesik},
     title = {Systems of first order {ODE} generating confluent {Heun} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--194},
     publisher = {mathdoc},
     volume = {485},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_485_a10/}
}
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A. A. Salatich; S. Yu. Slavyanov; O. L. Stesik. Systems of first order ODE generating confluent Heun equations. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 187-194. http://geodesic.mathdoc.fr/item/ZNSL_2019_485_a10/