Determination of Critical Behavior in Lattice Statistics from Series Expansions. I

A method is developed for determining the critical point and the critical exponent from terms of a series expansion for a restricted class of functions. The advantage of the method is that under certain reasonable assumptions it provides estimates for errors which are narrower than those usually given. As examples, we consider the high-temperature susceptibility series for the Ising model and the analogous chain-generating function for the excluded volume problem.