Variational perturbation theory

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In mathematics, variational perturbation theory is a mathematical method to convert divergent power series in a small expansion parameter, say

s=\sum_{n=0}^\infty a_n g^n,

into a convergent series in powers

s=\sum_{n=0}^\infty b_n /(g^\omega)^n,

where ω is a critical exponent. This is possible with the help of variational parameters, which are determined by optimization order by order in g.

Variational perturbation theory is an important mathematical tool in the theory of critical phenomena. It has led to the most accurate predictions of critical exponents.

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