  We consider the problems of calculating the dynamical order parameter
two-point function at finite temperatures and the one-point function after a
quantum quench in the transverse field Ising chain. Both of these can be
expressed in terms of form factor sums in the basis of physical excitations of
the model. We develop a general framework for carrying out these sums based on
a decomposition of form factors into partial fractions, which leads to a
factorization of the multiple sums and permits them to be evaluated
asymptotically. This naturally leads to systematic low density expansions. At
late times these expansions can be summed to all orders by means of a
determinant representation. Our method has a natural generalization to
semi-local operators in interacting integrable models.
