Converting Divergent Weak-Coupling into Exponentially Fast Convergent Strong-Coupling Expansions

With the help of a simple variational procedure it is possible to convert the partial sums of order $N$ of many divergent series expansions $f(g)={\sum }_{n=0}^{\mathrm{\infty }}{a}_n{g}^n$ into partial sums $\sum_{n=0}^N b_n g^{- \omega n}$,where$0<\omega<1$ is a parameter that parametrizes the approach to the large-$g$ limit. The latter are partial sums of a strong-coupling expansion of $f(g)$ which converge against $f(g)$ for $g$ {\em outside} a certain divergence radius. The error decreases exponentially fast for large $N$, like $e^{-\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{.}\times N^{1-\omega }}$. We present a review of the method and various applications.