Variational perturbation theory

In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say s = ∑ n = 0 ∞ a n g n {\displaystyle s=\sum _{n=0}^{\infty }a_{n}g^{n}} , into a convergent series in powers s = ∑ n = 0 ∞ b n / ( g ω ) n {\displaystyle s=\sum _{n=0}^{\infty }b_{n}/(g^{\omega })^{n}} , where ω {\displaystyle \omega } is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in g {\displaystyle g} .

Source: Wikipedia — Variational perturbation theory (CC BY-SA 4.0)

Variational perturbation theory

In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say s = ∑ n = 0 ∞ a n g n {\displaystyle s=\sum _{n=0}^{\infty }a_{n}g^{n}} , into a convergent series in powers s = ∑ n = 0 ∞ b n / ( g ω ) n {\displaystyle s=\sum _{n=0}^{\infty }b_{n}/(g^{\omega })^{n}} , where ω {\displaystyle \omega } is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in g {\displaystyle g} .

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Source: Wikipedia "Variational perturbation theory" · CC BY-SA 4.0

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