Related papers: Multidimensional Pad\'e approximation of binomial …
In this article, we construct new Pad\'{e} approximations for the \emph{product} of binomial functions and powers of logarithmic functions. While several explicit Pad\'{e} approximants are known for powers of exponential functions, binomial…
We consider the Lommel functions $s_{\mu,\nu}(z)$ for different values of the parameters $(\mu,\nu)$. We show that if $(\mu,\nu)$ are half integers, then it is possible to describe these functions with an explicit combination of polynomials…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…
For a function $g\colon\{0,1\}^m\to\{0,1\}$, a function $f\colon \{0,1\}^n\to\{0,1\}$ is called a $g$-polymorphism if their actions commute: $f(g(\mathsf{row}_1(Z)),\ldots,g(\mathsf{row}_n(Z))) =…
The $(u,v)$-Pad\'e approximation to a function $f$ is the (unique, up to scaling) rational approximation $f(x) = P(x)/Q(x) + O(x^{u+v+1})$, where $P$ has degree $u$ and $Q$ has degree $v$. Motivated by recent work of Molin, Pazuki, and…
Let $E$ be a closed subset of the unit circle of measure zero. Recently, Beise and M\"uller showed the existence of a function in the Hardy space $H^2$ for which the partial sums of its Taylor series approximate any continuous function on…
The use of approximants of Pad\`e type are employed to develop a method aimed at opening new perspectives in the theory of Appell polynomials $a_n(x)$, specified by the generating function \sum_{n=0}^{\infty} \frac{t^n}{n!} a_n(x) = A(t)…
We give a Montessus de Ballore type theorem for row sequences of Hermite-Pad\'e approximations of vector valued analytic functions refining some results in this direction due to P.R. Graves-Morris and E.B. Saff. We do this introducing the…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
A subset $S$ of vertices of a graph $G$ is called a perfectly matchable set of $G$ if the subgraph induced by $S$ contains a perfect matching. The perfectly matchable set polynomial of $G$, first made explicit by Ohsugi and Tsuchiya, is the…
Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…
The theory of universal Taylor series can be extended to the case of Pad\'e approximants where the universal approximation is not realized by polynomials any more, but by rational functions, namely the Pad\'e approximants of some power…
Pad\'e approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. This work has evolved from the attempts to improve Baker-type linear independence measures, either by using the Bombieri-Vaaler version of…
Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights…
We construct explicitly Pad\'e approximations of the second kind for a special class of G-functions. These are then applied to prove a Baker-type lower bound for linear forms in the p-adic values of these functions. Moreover, we consider…
For trigonometric series and series of Chebyshev polynomials, we defined trigonometric Hermite-Pad\'e and Hermite-Jacobi approximations, linear and nonlinear Hermite-Chebyshev approximations. We established criterion of the existence and…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
The present paper deals with the convergence properties of multi-level Hermite-Pad\'e approximants for a class of meromorphic functions given by rational perturbations with real coefficients of a Nikishin system of functions, and study the…
Type I Hermite--Pad\'e polynomials for a set of functions $f_0, f_1, ..., f_s$ at infinity, $Q_{n,0}$, $Q_{n,1}$, ..., $Q_{n,s}$, is defined by the asymptotic condition $$…
In this paper, we estimate the linear independence measures for the values of a class Mahler functions of degree one and two. For the purpose, we study the determinants of suitable Hermite-Pad\'{e} approximation polynomials. Based on the…