A Fuchsian (differential) equation is a linear homogeneous ordinary differential equation with analytic coefficients in the complex domain whose singular points, including at infinity, are all regular singular points. In other words, it is the 1-dimensional case of the theory of meromorphic differential equations with only regular singular points. Hilbert's 21st problem is concerned with finding a Fuchsian equation with prescribed points of singularities and prescribed monodromies. The corresponding connection is also called Fuchsian.
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