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Existing methods of series analysis are largely designed to analyse thestructure of algebraic singularities. Functions with such singularities havetheir $n^{th}$ coefficient behaving asymptotically as $A \cdot \mu^n \cdotn^g.$ Recently, a number of problems in statistical mechanics and combinatoricshave been encountered in which the coefficients behave asymptotically as $B\cdot \mu^n \cdot \mu_1^{n^\sigma} \cdot n^g,$ where typically $\sigma =\frac{1}{2}$ or $\frac{1}{3}.$ Identifying this behaviour, and then extractingestimates for the critical parameters $B, \,\, \mu, \,\, \mu_1, \,\, \sigma,\,\, {\rm and} \,\, g$ presents a significant numerical challenge. We describemethods developed to meet this challenge.

Analysis of series expansions for non-algebraic singularities