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Fuchsian differential equations of order 3 with three singular points andwith an accessory parameter are studied. When local exponents are generic, noshift operator is found, for codimension-1 subfamilies, neither. We found shiftoperators for several codimension-2 subfamilies of which accessory parameter isassigned as a cubic polynomial in the local exponents. The Dotsenko-Fateevequation is one of them.

Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter II, Equations of order 3