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We present a method to sum Borel- and Gevrey-summable asymptotic series by matching the series to be summed with a linear combination of asymptotic series of known functions that themselves are scaled versions of a single, appropriate, but otherwise unrestricted, function $\Phi$. Both the scaling and linear coefficients are calculated from Pad\'e approximants of a series transformed from the original series by $\Phi$. We discuss in particular the case that $\Phi$ is (essentially) a confluent hypergeometric function, which includes as special cases the standard Borel-Pad\'e and Borel-Leroy-Pad\'e methods. A particular advantage is the mechanism to build knowledge about the summed function into the approximants, extending their accuracy and range even when only a few coefficients are available. Several examples from field theory and Rayleigh-Schr\"odinger perturbation theory illustrate the method., Comment: 12 pages, 2 figures, Published version

We compare two alternative expansions for finite attractive wells. One of them is known from long ago and is given in terms of powers of the strength parameter. The other one is based on the solution of the equations of the Rayleigh–Schrödinger perturbation theory in a basis set of functions of period L. The analysis of exactly solvable models shows that although the exact solution of the problem with periodic boundary conditions yields the correct result when L → ∞ the coefficients of the series for this same problem blow up and fail to produce the correct asymptotic expansion., Facultad de Ciencias Exactas, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

The title problem is classical in ignition theory. Here it is solved by an asymptotic analysis in which the nondimensional activation energy is treated as a large parameter. Inert and reactive zones are identified, and a temperature peak develops in the latter during a stage of transition to ignition. A criterion of thermal runaway yields a formally correct asymptotic expansion for the ignition time which agrees with results of numerical integrations if the activation energy is sufficiently large.