scholarly journals Power series with sum-product Taylor coefficients and their resurgence algebra

2011 ◽  
pp. 35-200
Author(s):  
Jean Ecalle ◽  
Shweta Sharma
Keyword(s):  
Power Series ◽  
Taylor Coefficients

On the Taylor coefficients of rational functions

1956 ◽  
Vol 52 (1) ◽  
pp. 39-48 ◽  
Author(s):  
K. Mahler ◽  
J. W. S. Cassels
Keyword(s):  
Power Series ◽  
Rational Function ◽  
Rational Functions ◽  
Partial Solution ◽  
Convergent Power Series ◽  
Taylor Coefficients ◽  
Image Position

Let F(z) be a rational function of z which is regular at z = 0 and so possesses a convergent power seriesThe problem arises of characterizing those rational functions F(z) that have infinitely many vanishing Taylor coefficientsfh. After earlier and more special results by Siegel(2) and Ward(4) I applied in 1934(1) a p-adic method due to Skolem(3) to the problem and obtained the following partial solution.

DERIVATIVES FOR THE STABLE AND UNSTABLE MANIFOLDS OF A Cr Diffeomorphism ofR2

1993 ◽  
Vol 03 (06) ◽  
pp. 1601-1605 ◽  
Author(s):  
RAY BROWN ◽  
LEON CHUA
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Unstable Manifold ◽  
Taylor Polynomial ◽  
Stable And Unstable Manifolds ◽  
Taylor Coefficients ◽  
Unstable Manifolds

We illustrate how to form the Taylor polynomial for a stable or unstable manifold when considered as a curve in the plane. Our method does not use power series or assume that the manifold is analytic as is done in the method of Poincaré. Instead we use simple calculus to obtain closed form expressions for the Taylor coefficients.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

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