Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Padé approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential ...

Truncated perturbative series (TPS’s) of any observable have the unphysical dependence on the choice of the renormalization scale (RScl). The diagonal Padé approximants (dPA’s) to any TPS of an observable possess the favorable property of being invariant in the large-β0 limit. This means that they are invariant under the change of the RScl μ when the “running” coupling parameter αs(μ ) evolves ...

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so-called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the ...

The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: ~a! the introduction of two new energy-type and flux-type functions e(v) and f (v), respect...