This paper expresses the solutions given by T. Mandai [J. Math. Soc. Japan 52, 645–672 (2000; Zbl 0993.35004)], for a homogeneous Fuchsian partial differential equation (PDE) with holomorphic coefficients, in the form of an integral involving a kernel which is holomorphic for \(t\) in the universal covering of a pointed disc.