Системи степенів конформних відображень і біортогональні до них системи функцій: Fìz.-mat. model. ìnf. tehnol. 2016, 26:31-44

• Дата: 2018
• Автор: Ivasyk, Halyna
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2018
• Теми: біортогональні системи; конформне відображення; функціональні ряди; рівняння Гельмгольца
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/15
• Назва журналу: Physico-mathematical modeling and informational technologies

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. References Dzyadyk, V. K. (1977). Introduction to the theory of approximation of functions by polynomials. M .: Nauka. Leont'ev, A. F. (1980). Sequences of polynomials of exponential functions. M .: Science. Markushevich, A. I. The theory of analytic functions. Volume 2. M .: Nauka. Smirnov, V. I, Lebedev, N. A. (1964). The constructive theory of complex functionsAC. M .: Science. 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. Suhorolsky, M. A., & Lukovskii, І.O., Kіt, G.S., Kushnіr, R.M. (Eds.). (2014). Analytical solutions of Helmholtz equation. Matematichnі problemi mechanіki neodnorіdnih agencies, 160-163. Sukhorolsky, M. A, Dostoyna, V. V. (2013). One class of biorthogonal systems of functions that arise in the solution of the Helmholtz equation in the cylindrical coordinate system. J. Math. Sci., 192(5), 541-554. DOI https://doi.org/10.1007/s10958-013-1415-5 Korn, G. A., Korn, T. M. (2000). Mathematical Handbook for Scientists and Engineers. DOVER PUBLICATIONS, INC: Mineola, New York. Lavrent'ev, M. A., Shabat, B. V. (1987). Methods of complex function theory. M .: Nauka.