Related papers: Taylor expansions over generalised power series
In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
A holomorphic function f on a simply connected domain {\Omega} is said to possess a universal Taylor series about a point in {\Omega} if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside…
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.
The function $y=\Phi_\alpha(x)$, the solution of $y^\alpha e^y=x$ for $x$ and $y$ large enough, has a series expansion in terms of $\ln x$ and $\ln\ln x$, with coefficients given in terms of Stirling cycle numbers. It is shown that this…
We give an overview about the power product expansion of the exponential series and derive some q-analogs
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method. In the…
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and…
We present a characterization of sets for which Cartwright's theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.
An exact series expansion for the field radiated by a monopole ring source with angular variation in source strength is derived from a previously developed expression for the field from a finite disk. The derived series can be used…
This is a preprint of 1992 with some updates. We study sections of the exponential function Taylor series. Interesting inequalities for these sections were considered by G.Hardy, Kesava Menon, W. Gautschi, H.Alzer and others. The main aim…
A new series expansion for the function (arctan(x)/x)^n is developed and some properties of the expansion coefficients are obtained.
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values…
In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear.
A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a…