The convergence of (diagonal) sequences of rational interpolants to an analytic function is investigated. Problems connected with their definition are shortly discussed. Results about locally uniform convergence are reviewed. Then the convergence in capacity is studied in more detail. Here, a central place is taken by a theorem about the convergence in capacity of rational interpolants to funct...

We show that the differential transform is well known Taylor series (contrary to what authors claim) and method (DTM) Frobenius method, commonly used obtain exact or approximate solutions equations. The generalized (GTM) merely application of Padé approximants produced by method. argue particular differential-difference nonlinear equations are scarce utility because initial conditions not flexi...

The current algorithms use either the full form or Schur decomposition of matrix in inverse scaling and squaring method to compute logarithm. consists two main calculations: taking a square root evaluating Padé approximants. In this work, we suggest using structure preserving iteration as an alternative Denman-Beavers for root. Numerical experiments show that while preserves Hamiltonian logarit...

We show how one can use Hermite-Padé approximation and little q-Jacobi polynomials to construct rational approximants for ζq(2). These numbers are qanalogues of the well known ζ(2). Here q = 1 p , with p an integer greater than one. These approximants are good enough to show the irrationality of ζq(2) and they allow us to calculate an upper bound for its measure of irrationality: μ (ζq(2)) ≤ 10...

The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field theory. We observe that the rate of convergence can be improved by the application of Padé approximants to the Borel transform expressed as a function of the co...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

Starting from a strong Stieltjes distribution φ, general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution φ and two-point Padé approximants to the Stieltjes transform of φ is revisited. Finally, illustrative numeri...