On calculating partial sums of multiple numerical series by methods of Computer Algebra

V. I. Kuzovatov; Кузоватов В. И.; А. А. Kytmanov; Кытманов А. А.; Е. К. Myshkina; Мышкина Е. К.

doi:10.31857/S0132347424020094

On calculating partial sums of multiple numerical series by methods of Computer Algebra

Autores: Kuzovatov V.I.¹, Kytmanov А.А.¹^,2, Myshkina Е.К.¹
Afiliações:
1. Siberian Federal University
2. MIREA — Russian Technological University
Edição: Nº 2 (2024)
Páginas: 74-78
Seção: КОМПЬЮТЕРНАЯ АЛГЕБРА
URL: https://cardiosomatics.ru/0132-3474/article/view/675707
DOI: https://doi.org/10.31857/S0132347424020094
EDN: https://elibrary.ru/ROLFAU
ID: 675707

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Sobre autores
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Resumo

A method to calculate partial sums of some multiple numerical series arising when searching for the resultant of a polynomial and an entire function is proposed. One can apply a symbolic algorithm that uses recurrent Newton formulas to find power sums of roots included in this formula without finding the very roots of the system. The algorithm that implements the proposed approach to calculate partial sums of multiple numerical series is implemented in Maple. Examples of using this algorithm to find partial sums of some classes of multiple numerical series are given.

Palavras-chave

multiple numerical series, power sums of roots, recurrent Newton formulas, methods of Computer Algebra

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Bibliografia

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Aizenberg L.A., Yuzhakov A.P. Integral’nye predstavleniya i vychety v mnogomernom kompleksnom analize (Integral Representations and Residues in Multidimensional Complex Analysis), Novosibirsk: Nauka, 1979.
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Tsikh A.K. Multidimensional residues and their applications, AMS, Providence, 1992.
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Myshkina E.K. Some examples of finding the sums of multiple series // J. Siberian Federal Univ. Math. Phys. 2014. V. 7. № 4. P. 515–529.
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Kytmanov A.A., Kytmanov A.M., Myshkina E.K. Residue integrals and Waring’s formulas for algebraic or even transcendental systems // Complex Variables and Elliptic Equations. 2019. V. 64. № 1. P. 93–111.
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