Self-Similar Exponential Approximants

Details Self-Similar Exponential Approximants Self-Similar Exponential Approximants

1998-09-13

arxiv.org/abs/cond-mat/9809183v1

Phys.Rev. E58 (1998) 1359-1382

Physics

Condensed Matter

Statistical Mechanics

1 file, 37 pages, RevTex, 1 table

Scientific paper

10.1103/PhysRevE.58.1359

An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed. The basis of this construction is the self-similar approximation theory. Control functions governing the convergence of exponentially renormalized series are defined from stability and fixed-point conditions and from additional asymptotic conditions when the latter are available. The stability of the calculational procedure is checked by analyzing cascade multipliers. A number of physical examples for different statistical systems illustrate the generality and high accuracy of the approach.

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