The theorem proved here extends the author's previous work on Chebyshev series [4] by showing that if f(x) is a member of the class of so-called "Stieltjes functions" whose asymptotic power series 2 anx" about x = 0 is such that ttlogjaj _ hm —;-= r, «log n then the coefficients of the series of shifted Chebyshev polynomials on x e [0, a],2b„Tf(x/a), satisfy the inequality 2 . m log | (log |M) ...

in this paper, an integration of a symbolic power series method - padé approximation technique (ps - padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. as both boundary conditions tended to infinity, the combination of series solut...

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and positivity of the corresponding quadrature coe...

In this work type II Hermite-Padé approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.

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.

A modified Padé approximant is used to construct an equation of state, which has the same large-density asymptotic behavior as the model fluid being described, while still retaining the low-density behavior of the virial equation of state (virial series). Within this framework, all sequences of rational functions that are analytic in the physical domain converge to the correct behavior at the s...