We present a method in which the Padé approximant is used to calculate the asymptotic
behavior of a function from the first few terms of its power series. We illustrate this method by …

What's in a name? To paraphrase Shakespeare's Juliet, that which-ilie Haynsworth called
the Schur complement, by any other name would be just as beautiful. Nevertheless, her …

A review is presented of the most effective methods for the computation of Sommerfeld
integral tails. Such integrals, which are often oscillatory, singular and divergent, commonly …

“The career structure and funding of the universities [...] currently strongly discourages
academics and faculties from putting any investment into teaching–there are no career or …

This review is focused on the borderline region of theoretical physics and mathematics. First,
we describe numerical methods for the acceleration of the convergence of series. These …

An important problem that arises in many scientific and engineering applications is that of
approximating limits of infinite sequences which in most instances converge very slowly …

Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the
liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples …

Singular perturbation methods, such as the method of multiple scales and the method of
matched asymptotic expansions, give series in a small parameter ε which are asymptotic but …

A review is presented of the extrapolation methods for accelerating the convergence of
Sommerfeld-type integrals (ie semi-infinite range integrals with Bessel function kernels) …

The classical Sommerfeld half-space problem is revisited, with generalizations to multilayer
and plasmonic media and focus on the surface field computation. A new ab initio solution is …