An application of the exactified Poincaré asymptotic expansion of the Hankel integral to thin film thermography

Abstract

We use the distribution approach to asymptotics to obtain an asymptotic expansion of the Hankel integral appearing in the theory of thermal diffusivity of polymer thin films for arbitrarily large values of the asymptotic parameter. We find that the method recovers exponentially small terms in the asymptotic expansion of the Hankel integral, and yields the exactification of the Poincaré expansion. The expansion is then applied to moderate and small values of the parameter. It is demonstrated that the exactified expansion yields a much more accurate approximation of the Hankel integral than the power-type asymptotic expansion for non-large values of the parameter.