Related papers: Generalization of the Taylor formula
This short note provides an explicit description of the Fr\'echet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fr\'echet derivatives of…
We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
We extend the usual definition of the derivative in a way that Calculus I students can easily comprehend and which allows calculations at branch points.
This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of $q$-ary expansions.
The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied.…
We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
The Lambert $W$ function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In the last decade it…
In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.