Each component of any solution of a Fuchsian differential system satisfies a Fuchsian differential equation. The set of Fuchsian systems is fibered into equivalence classes. Each class consists of systems with similar sets of matrix residues, the conjugation matrix being the same for all elements of the set. We investigate the corresponding classes of scalar equations.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 468, 2018, pp. 221–227.
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Babich, M.V., Slavyanov, S.Y. Relations Between Second-Order Fuchsian Equations and First-Order Fuchsian Systems. J Math Sci 240, 646–650 (2019). https://doi.org/10.1007/s10958-019-04381-z
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DOI: https://doi.org/10.1007/s10958-019-04381-z