Jonathan Eckstein, Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming, Mathematics of Operations Research, Vol. 18, No. 1 (Feb., 1993), pp. 202-226 ...

We derive a formula for an n-th order divided difference of the inverse of a function. The formula has a simple and surprising structure: it is a sum over partitions of a convex polygon with n + 1 ...