  Several results on Heun's equation are generalized to a certain class of
Fuchsian differential equations. Namely, we obtain integral representations of
solutions and develop Hermite-Krichever Ansatz on them. In particular, we
investigate linear differential equations that produce Painlev\'e equation by
monodromy preserving deformation and obtain solutions of the sixth Painlev\'e
equation which include Hitchin's solution. The relationship with finite-gap
potential is also discussed.
