Related papers: Taylor expansions over generalised power series
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.
Cartesian differential categories provide a categorical framework for multivariable differential calculus and also the categorical semantics of the differential $\lambda$-calculus. Taylor series expansion is an important concept for both…
This paper concerns pairs of models of the theory of the differential field of logarithmic-exponential transseries that are tame as a pair of real closed fields. That is, the smaller model is bounded inside the larger model and there exists…
In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation. We…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tanx, several expressions for log coshx and an identity for {\pi}2, from a series expansion of tan x, which gives the…
For noncommutative variables x,y an expansion of log(exp(x)exp(y)) in powers of x+y is obtained.Each term of the series is given by an infinite sum in powers of x-y.The series is represented by diagrams.
The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…
An effective radius of convergence is defined and computed for any truncated Taylor series. Applications to well known series are performed and is shown that a range of good coincidence for actual and approximative plot can always be found.…
Has it ever occurred to you that the kinematic equations for uniformly accelerated one-dimensional motion are Taylor series expansions? If not, you are in good company. I didn't know this myself until a colleague pointed it out to me many…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…