= Fuchsian linear differential system
{c}
{title2=$F'=A(z)F,\qquad A(z)=R/(z-a)+H(z)$}
In a fixed frame, a first-order <linear differential equation> is Fuchsian at a finite point when its coefficient matrix has at most a <simple pole> there. Its residue is $R$. The global object is the matrix-valued one-form $A(z)\,dz$: in the coordinate $t=1/z$ its coefficient is $-t^{-2}A(1/t)$. A Fuchsian system has intrinsic <regular singular points>, but an intrinsically regular singular system may have higher-order coefficient poles in a different meromorphic frame.
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