Analyticity of the d-Dimensional Bond Percolation Probability Around p=1

Let (p) be the percolation probability of a d-dimensional bond percolation process on Z ^d . We prove that 1–(p) can be written as an absolutely convergent series in powers of (1–p)/p, provided that |(1–p)/p| is sufficiently small. This implies that (p) is an analytic function of the complex variable p, around p=1.