A recurrence technique for confluent singularity analysis of power series

Abstract

A generalisation of the recurrence method of series analysis is developed which permits the analysis of power-law confluent singularities in a function from its expansion in a power series. This method yields directly critical points and associated exponents for each element of an array of Kth-order, inhomogeneous, differential equation approximants (M₀,M₁,...M_K;L). Biased approximants are also discussed. Tests are presented which show that the method can be superior to the Dlog Pade approximant for determining the dominant critical exponent in a function known to have confluent singularities, and can yield good approximations for the leading confluent exponent. An application to the problem of determining correction-to-scaling exponents in 3D spin- infinity Ising models yields results in agreement with other studies.