Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if th...

Based on a “monotonicity” analogue of the l’Hospital Rule, monotonicity properties of the relative error are established for a Padé approximation of Mills’ ratio.

In Fitzpatrick and Flynn (J. Symbolic Comput. 13 (1992) 133), a Gröbner basis technique for multivariable Padé approximation problems was developed under a rather restrictive hypothesis on the shape of the numerator and denominator in relation to the approximation conditions desired. In this article, we show that their hypotheses can be replaced by other less stringent conditions, and we show h...

It is proved that among the rational iterations locally converging with order s > 1 to the sign function, the Padé iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator.

We solve the equation of the title for q = 3 and, partially, for q = 2. These are the only prime values of q for which there exist integer solutions. Our arguments are based upon off-diagonal Padé approximation to the binomial function.

In this paper, approximate analytical solution of SIRC model associated with the evolution of influenza A disease in human population is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and padé approximant. The MDTM is used to increase the a...

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...

Analogues of the Nuttall-Pommerenke theorem and Wallin-type theorems for classical Pade approximants, are proved for linear and nonlinear Pade approximants formed from series of orthogonal polynomials, corresponding to a distribution da(x) with at most finitely many sign changes.

We have developed two types of mechanical models of the human vocal tract. The first model was designed for the retroflex approximant [r] and the alveolar lateral approximant [l]. It consisted of the main vocal tract and a flapping tongue, where the front half of the tongue can be rotated against the palate. When the tongue is short and rotated approximately 90 degrees, the retroflex approximan...

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.