Algebraic approximants: a new method of series analysis

Abstract

The authors propose a new method of series analysis in which the available series coefficients are fitted to an algebraic equation. Such a proposal restricts solutions to have algebraic singularities with rational critical exponents. The advantage of the method over the method of differential approximants is that in those cases where the two methods are exact, the algebraic approximant method usually (though not invariably) requires far fewer series coefficients for its exact specification, and hence discovery. The method is therefore potentially valuable in the study of two-dimensional critical systems in particular.