Abstract
Ordinary linear homogeneous second-order differential equations with polynomial coefficients including one in front of the second derivative are studied. Fundamental definitions for these equations: of s-rank of the singularity (different from Poincaré rank), of s-multisymbol of the equation, and of s-homotopic transformations are proposed. The generalization of Fuchs' theorem for confluent Fuchsian equations is proved. The tree structure of types of equations is shown, and the generalized confluence theorem is proved.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 233–247, August, 1995.
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Seeger, A., Lay, W. & Slavyanov, S.Y. Confluence of fuchsian second-order differential equations. Theor Math Phys 104, 950–960 (1995). https://doi.org/10.1007/BF02065975
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DOI: https://doi.org/10.1007/BF02065975