METHOD OF OBTAINING APPROXIMATE FORMULAS
Journal Title: EUREKA: Physics and Engineering - Year 2018, Vol 0, Issue 2
Abstract
The two-parameter method of approximating the sum of a power series in terms of its first three terms of the expansion, which allows one to obtain analytic approximations of various functions, decomposes into a Maclaurin series. As an approximation function of this approximation, it is proposed to use elementary functions constructed in the Nth degree, but with a "compressed" or "stretched" variable x due to the introduction of the numerical factor M (x ≡ ε ∙ m, M ≠ 0) into it. The use of this method makes it possible to significantly increase the range of very accurate approximation of the obtained approximate function with respect to a similar range of the output fragment of a series of three terms. Expressions for both the approximation parameters (M and N) are obtained in a general form and are determined by the coefficients of the second and third terms of the Maclaurin series. Also expressions of both approximation parameters are found for the case if the basis function and the approximant function decompose into the Maclaurin series in even powers of the argument. A number of examples of approximation of functions on the basis of the analysis of power series into which they decompose are given.
Authors and Affiliations
Konstantin Ludanov
Keywords
Related Articles
- EP ID EP669017
- DOI 10.21303/2461-4262.2018.00589
- Views 235
- Downloads 0
RESEARCH OF MICROBIOLOGICAL INDICATORS OF QUALITY OF SURFACE WATERS OF NATURAL ENVIRONMENTAL TERRITORIES OF THE DANUBE BASIN
A comparative analysis of the sanitary and ecological state of surface watercourses in the upper part of the Danube basin (on theterritoryofUkraine) was carried out according to microbiological indicators. Similar hygien...
METHOD OF OBTAINING APPROXIMATE FORMULAS
The two-parameter method of approximating the sum of a power series in terms of its first three terms of the expansion, which allows one to obtain analytic approximations of various functions, decomposes into a Maclaurin...
ANALITIC INVESTIGATION OF THE REGULARITIES OF CHANGING DUST CONCENTRATION DURING THE ABRASIVE DECREASE OF STONE STRUCTURES
In the process of repair or restoration of building structures, it is often necessary to strengthen building structures from limestone-shell rock, concrete, reinforced concrete, hard materials-granite, basalt, etc. by cu...
INVESTIGATION OF THE NON-EQUILIBRIUM IMPACT ON THE PROPERTIES OF A SUPERCONDUCTOR USING A PLASMA SUPERCONDUCTIVITY MECHANISM
The results of theoretical studies of a semiconductor structure are presented which, upon irradiation with a particle stream or light, transforms into a superconducting phase state. The work is carried out: – analysis...
PROACTIVE DEVELOPMENT OF ORGANIZATIONAL STRUCTURE OF TERRITORIAL DEVELOPMENT PROJECT WITH USING BI-ADAPTIVITY
The article presents the scientific task of developing models and methods of proactive development of the organizational structure of territorial development projects using bi-adaptivity. Literary sources are analyzed. T...