Analysis of series expansions for non-algebraic singularities

2014/05/21 by Anthony J Guttmann · 2 citations
Mathematics · Computer Science · #Mathematical functions and polynomials #Polynomial and algebraic computation #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.1088/1751-8113/48/4/045209

Abstract

Existing methods of series analysis are largely designed to analyse the structure of algebraic singularities. Functions with such singularities have their n^th coefficient behaving asymptotically as A ⋅ μⁿ ⋅ n^g. Recently, a number of problems in statistical mechanics and combinatorics have been encountered in which the coefficients behave asymptotically as B ⋅ μⁿ ⋅ μ₁^nσ ⋅ n^g, where typically σ= (1)/(2) or (1)/(3). Identifying this behaviour, and then extracting estimates for the critical parameters B, μ, μ₁, σ, \rm and g presents a significant numerical challenge. We describe methods developed to meet this challenge.

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