We obtain a result on convergence of Padé approximants for meromorphic functions of Stieltjes type. Connection of Padé approximants with Stieltjes moment problem plays a key role in the proof.

We discuss how to implement an " environmentally friendly " renormalization in the context of finite temperature field theory. Environmentally friendly renormalization provides a method for interpolating between the different effective field theories which characterize different asymptotic regimes. We give explicit two loop Padé resummed results for λφ 4 theory for T > T c. We examine the impli...

Utilizing asymptotic Padé-approximant methods, we estimate the three-loop order MS coefficients of α s [log(μ/m b (μ)] terms [k = {0, 1, 2, 3}] within the b → ulνl decay rate. Except for the coefficient of the k = 0 term, all other coefficients may also be obtained via renormalization-group (RG) methods. The relative errors in asymptotic Padé-approximant estimates of the k = {1, 2, 3} terms are...

We give a new algorithm for the construction of unique superoptimal analytic approximant given continuous matrix-valued function on unit circle, making use exterior powers operators in preference to spectral or {\em Wiener-Masani} factorizations.

In relation to Fourier-Pade approximation, Ed Sa¤ observed that Taylor and Lagrange interpolation projections satisfy the following property: P (f) P (g) 2 n =) P (f g) = P (f) P (g). We classify all projections that satisfy this property, thus answering a question of Sa¤. Some error formulas for approximation with the above mentioned projections are also produced. AMS Subject Classi…cation: 41...

We propose a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result of the considered approach, we prove a convergen...

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.