= Fuchs' theorem
{wiki=Fuchs'_theorem}
Fuchs' theorem is a result in the field of complex analysis, particularly in the study of ordinary differential equations with singularities. The theorem provides conditions under which a linear ordinary differential equation with an irregular singular point can be solved using power series methods. Specifically, Fuchs' theorem states that if a linear differential equation has only regular singular points, then around each regular singular point, there exist solutions that can be expressed as a Frobenius series.
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