Related papers: Taylor expansions over generalised power series

The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…

We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…

We prove new variants of the Lambert series factorization theorems studied by Merca and Schmidt (2017) which correspond to a more general class of Lambert series expansions of the form $L_a(\alpha, \beta, q) := \sum_{n \geq 1} a_n q^{\alpha…

Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…

This paper deals with a group of generalized power series associated to any augmented operad, focusing on the case of the PreLie operad. The solution of flow equations using the pre-Lie structure on vector fields on an affine space gives…

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, therefore the whole series, converge to zero much more…

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an…

We establish Taylor series expansions in rational (and elliptic) function bases using E. Rains' elliptic extension of the Askey-Wilson divided difference operator. The expansion theorem we consider extends M.E.H. Ismail's expansion for the…

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 $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of…

In this paper we study the isotropisation of a Generalized Scalar-Tensor theory with a massive scalar field. We find it depends on a condition on the Brans-Dicke coupling function and the potential and show that asymptotically the metric…

We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending…

Using a recent Mergelyan type theorem for products of planar compact sets we establish generic existence of Universal Taylor Series on products of planar simply connected domains Omegai, i=1, . . . , d. The universal approximation is…

We give an explicit implicit function theorem for formal power series that is valid for all fields, which implies in particular Lagrange inversion formula and and Flajolet-Soria coefficient extraction formula known for fields of…

We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincar\'e resonance in terms of asymptotic differential algebra, we give conditions for conjugacy of parabolic flat…

The generating series associated to a certain sequence of limited Taylor expansions coincides with the continuously iterated Invert Transform and displays thus a nice functional equality.