Extracting singularity structure from perturbation series

EXTRACTING SINGULARITY STRUCTURE FROM PERTURBATION SERIES 

A systematic approach to constructing approximants was proposed by Fade [24,25]. A set of polynomials where k indicates the degree of 

The notation O(z ) means that the coefficients of the Taylor series of the left-hand side are equal to zero up ffirough order K - 1. E in equation (4) represents the perturbation series of the energy function. Collecting terms according to the power of z yields K linear equations for die isT + 1 coefficients of the polynomials. The final coefficient is set according to an arbitrary normalization condition, typically, = 1. Once the poly- 

More appropriate are quadratic approximants [7,27-32], with M = 2, which have the double-valued solution 

Other kinds of approximants can also be used. For example, Olsen et al. [20] analyzed MP series convergence using a 2 X 2 matrix eigenvalue equation [38,39], which implicitly incorporates a square-root branch point. It is of course possible simply to explicitly construct an approximant as an arbitrary function with the singularity structure that E z) is expected to have. We suggest, for example, approximants of the form  

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Extracting singularity structure from perturbation series... 

EXTRACTING SINGULARITY STRUCTURE FROM PERTURBATION SERIES... 

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