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) = ∑∞ n=0 ang n into partial sums ∑N n=0 bng −ωn, where 0 < ω < 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 outside a certain divergence radius. The error decreases exponentially fast for large N , like e−const.×N . We present a review of the method and various applications. c © Electronic Journal of Theoretical Physics. All rights reserved.