In 1961, Baker, Gammel and Wills formulated their famous conjecture that if a function f is meromorphic in the unit ball, and analytic at 0, then a subsequence of its diagonal Padé approximants converges uniformly in compact subsets to f . This conjecture was disproved in 2001, but it generated a number of related unresolved conjectures. We review their status.

Using a convergence theorem for Fourier-Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard’s theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szegő functions.

The relation between the on-shell and MS mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in o...

We obtain results on the convergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on unbounded intervals. These theorems extend some results given by Guillermo López in this direction substituting the Carleman condition in his theorems by the determination of the corresponding moment problem. c © 2009 Elsevier Inc. All right...

Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet. Keywords—Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.

We calculate the pion decay constant near the critical temperature of the O(N) nonlinear sigma model in the large N limit. Making use of the known low temperature behavior, we construct a Padé approximant to obtain the behavior of fπ(T ) at all temperatures.

In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix multiplication: most other fast approximant basis algorithms basically aim at efficiently reducing the input instance to instances for which PMBasis is fast. Such red...