In this paper we prove a conjecture on a common region of a convergence of Padé iterations for the matrix sector function. For this purpose we show that all Padé approximants to a special case of hypergeometric function have a power series expansion with positive coefficients. Using a sharpened version of Schwarz’s lemma, we also demonstrate a better estimate of the convergence speed. Our resul...

Using sequence transformation and extrapolation algorithms for the prediction of further sequence elements from a finite number of known sequence elements is a topic of growing importance in applied mathematics. For a short introduction, see the book of Brezinski and Redivo Zaglia 1, Section 6.8 . We mention theoretical work on prediction properties of Padé approximants and related algorithms l...

A detailed analysis to the [1,2] Padé approximation to the ππ scattering 2–loop amplitudes in chiral perturbation theory is made.

A numerical method for solving the Flierl–Petviashivili (FP) equation and its variants is proposed. The proposed scheme is based on differential transform method (DTM) and Padé approximants. The DTM-Padé technique introduces an alternative framework designed to overcome the difficulty of the singular point at x = 0. The numerical results demonstrates the validity and applicability of the method...

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, f ∈ A (C \A), ]A < ∞. J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f . The Padé approxi...

This work is about Frobenius-Padé approximants for series of orthogonal polynomials of dimension d (d ∈ N). Concerning to the series, we give the projection property of partial sums, we show how to compute their coe cients, and how to get the coe cients of the product of a series by a polynomial. Concerning to the approximants we work essentially about their recursive computation. Also, we give...

In this paper, we propose a new approach to solve the unsteady gas equation. We apply the Modified Laplace decomposition method (MLDM) coupled with Pade ́ approximation to compute a series solution of unsteady flow of gas through a porous medium. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The nonlinear terms can be easil...

w x Ž . In 1948, Paul Erdos E1 proved the irrationality of h 1 . Recently, ̋ 2 w x Peter Borwein used Pade approximation techniques B1 and some coḿ w x Ž . plex analysis methods B2 to prove the irrationality of both h 1 and q Ž . Ln 2 . Here we present a proof in the spirit of Apery’s magnificent proof ́ q Ž . w x of the irrationality of z 3 A , which was later delightfully accounted by w x Alf v...

We investigate the convergence of the rows (fixed denominator degree) of the Walsh array of best rational approximants to a meromorphic function. We give an explicit algorithm for determining when convergence is guaranteed and obtain rates of convergence.in the appropriate cases. This algorithm also provides the solution to an integer programming problem that arises in the study of Pade approxi...

In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Padé approximations are given as particular cases. As a consequence, such approximations can be derived directly by power matrices. Moreover, Rédei rational functions are introduced as convergents of particular periodic continued fractions and are applied for ...