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

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

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.

Sobre autores

V. Kuzovatov

Siberian Federal University

Autor responsável pela correspondência
Email: kuzovatov@yandex.ru
Rússia, Krasnoyarsk

А. Kytmanov

Siberian Federal University; MIREA — Russian Technological University

Email: aakytm@gmail.com
Rússia, Krasnoyarsk; Moscow

Е. Myshkina

Siberian Federal University

Email: elfifenok@mail.ru
Rússia, Krasnoyarsk

Bibliografia

  1. Aizenberg L.A. On one formula of generalized logarithmic residue and solution of the system of nonlinear equations, Dokl. Akad. Nauk SSSR (Proc. of the USSR Academy of Sciences). 1977. V. 234. № 3. P. 505–508.
  2. 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.
  3. Bykov V.I., Kytmanov A.M., Lazman M.Z. Elimination methods in polynomial computer algebra, Kluwer Academic Publishers, Dodrecht-Boston-Basel, 1998.
  4. Tsikh A.K. Multidimensional residues and their applications, AMS, Providence, 1992.
  5. Bykov V.I., Tsybenova S.B. Nelineinye modeli khimicheskoi kinetiki (Nonlinear Models of Chemical Kinetics), Moscow: KRASAND, 2011.
  6. 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.
  7. Kytmanov A.A., Kytmanov A.M., Myshkina E.K. Finding Residue Integrals for Systems of Non-algebraic Equations in Cn // Journal of Symbolic Computation. 2015. V. 66. P. 98–110.
  8. 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.
  9. Kytmanov A.M., Myshkina E.K. On Some Approach for Finding the Resultant of Two Entire Functions // J. Siberian Federal Univ. Math. Phys. 2019. V. 12. № 4. P. 434–438.
  10. Kytmanov A.M., Myshkina E.K. On Finding the Resultant of Two Entire Functions // Probl. Anal. Issues Anal. 2020. V. 9. № 3. P. 119–130.
  11. Kytmanov A.A. Analogues of recurrent Newton formulas, Russian Math. 2009. V. 53. P. 34–44.
  12. Kytmanov A.A. An algorithm for calculating power sims of roots for a class of systems of nonlinear equations // Programming and Computer Software. 2010. V. 36. № 2. P. 103–110.
  13. Bryuno A.D., Batkhin A.B. Algorithms and programs for calculating the roots of polynomial of one or two variables // Programming and Computer Software. 2021. V. 47. № 5. P. 353–373.
  14. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integraly i ryady. Elementarnye funktsii (Integrals and Series. Elementary Functions), Moscow: Nauka, Gl. red. fiz.-mat. lit, 1981.

Declaração de direitos autorais © Russian Academy of Sciences, 2024

Este site utiliza cookies

Ao continuar usando nosso site, você concorda com o procedimento de cookies que mantêm o site funcionando normalmente.

Informação sobre cookies