A recursion formula for the correlation functions of an inhomogeneous XXX model

A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneity parameters. Our formula allows for a direct proof of this structure, as well as an exact description of the rational functions which has been left undetermined in the previous works.