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Fuchsian System


A system of linear differential equations

 (dy)/(dz)=A(z)y,
(1)

with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of order 1 at a_j for j=1, ..., N. A system is Fuchsian iff there exist n×n matrices B_1, ..., B_N with entries in Z such that

 A(z)=sum_(j=1)^N(B_j)/(z-a_j)
(2)
 sum_(j=1)^NB_j=v.
(3)

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Cite this as:

Weisstein, Eric W. "Fuchsian System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FuchsianSystem.html

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