We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore’s and Gonchars’s theorems on the convergence of rows of Padé approximants are proved.

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...

A 1961 conjecture of Baker, Gammel and Wills asserts that if a function f is meromorphic in the unit ball, and analytic at 0, then a subsequence of its diagonal Pade approximants converges uniformly in compact subsets omitting poles. Inasmuch as the denominators of the Padé approximants are complex orthogonal polynomials, and the convergence of sequences of Padé approximants is determined large...

We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes c...

Padé-type approximants are rational functions that approximate a given formal power series. Boutry [Numer. Algorithms, 33 (2003), pp 113–122] constructed correspond to the averaged Gauss quadrature rules introduced by Laurie [Math. Comp., 65 (1996), pp. 739–747]. More recently, Spalević 76 (2007), 1483–1492] proposed optimal rules, have higher degree of precision than corresponding with...