The system of powers of conformal mappings and biorthogonal to them systems of the functions-Reference-Cited by-同舟云学术

The system of powers of conformal mappings and biorthogonal to them systems of the functions

Published:2017-12-30 Issue:26 Volume: Page:31-44
ISSN:1816-1545
Container-title:Physico-mathematical modelling and informational technologies
language:
Short-container-title:Fìz.-mat. model. ìnf. tehnol.

Author:

Ivasyk Halyna¹

Affiliation:

1. Lviv Polytechnic National University, S. Bandera str., 12, 79013, Lviv, Ukraine

Abstract

In this article we review the methods of power summation of factors. The degree of factors which are arbitrary powers of summation indices are considered. We show that using the Poisson-Abel method only those series can be summarized the order of member increase of which is proportional to the exponent depending on the summation index. At the same time the Gauss-Weierstrass method and other power factors methods can be also applied to the series the terms of which increase in proportion to the exponential dependence of the indices summation.

Publisher

National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka)

Reference9 articles.

1. Dzyadyk, V. K. (1977). Introduction to the theory of approximation of functions by polynomials. M .: Nauka.

2. Leont'ev, A. F. (1980). Sequences of polynomials of exponential functions. M .: Science.

3. Markushevich, A. I. The theory of analytic functions. Volume 2. M .: Nauka.

4. Smirnov, V. I, Lebedev, N. A. (1964). The constructive theory of complex functionsAC. M .: Science.

5. Suhorolsky, M. A. (2010). Development of the functions for system of polynomials, biorthohonal on closed contour of a system of regular at infinity far point of the function. Ukr. mat. Zh., 62(2), 238-254.