On calculation of power sums of roots for one class of systems of non-algebraic equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 190-209.

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The aim of this paper is evaluation power sums of roots in negative degree for systems of non-algebraic equations containing from entire functions of finite order of growth.
Keywords: non-algebraic systems of equations, order of growth entire functions, power sums of roots in negative degree.
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A. M. Kytmanov; E. K. Myshkina. On calculation of power sums of roots for one class of systems of non-algebraic equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 190-209. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a81/

[1] L. A. Aizenberg, “On a formula of the generalized multidimensional logarithmic residue and the solution of system of nonlinear equations”, Sov. Math. Doc., 18 (1977), 691–695 | MR

[2] L. A. Aizenberg, A. P. Yuzhakov, Integral representations and residues in multidimensional complex analysis, Trans. Amer. Math. Monographs, AMS, Providence, 1983 | MR

[3] A. K. Tsikh, Multidimensional residues and their applications, Translations of Mathematical Monographs, 103, American Mathematical Society, Providence, RI, 1992 | MR

[4] V. Bykov, A. Kytmanov, M. Lazman, M. Passare (eds.), Elimination Methods in Polynomial Computer Algebra, Math. and Appl., 448, Kluwer Acad. Publ., Dordrecht–Boston–London, 1998 | MR

[5] A. K. Tsikh, “Bezout theorem in the space of theory function. On solution of systems of algebraic equations”, Nekotorye voprosy mnogomernogo kompleksnogo analiza, Institut fiziki SO AN SSR, Krasnoyarsk, 1980, 185–196 (in Russian) | MR

[6] A. M. Kytmanov, Z. E. Potapova, “Formulas for determining power sums of roots of systems of meromorphic functions”, Izvestiya VUZ. Matematika, 49:8 (2005), 36–45 (in Russian) | MR

[7] V. I. Bykov, A. M. Kytmanov, S. G. Myslivets, “Power sums of nonlinear systems of equations”, Docl. Math., 76:2 (2007), 641–645 | MR

[8] A. M. Kytmanov, E. K. Myshkina, “Evaluation of power sums of roots for systems of non-algebraic equations in $\mathbb C^n$”, Russian Mathematics, 57:12 (2013), 31–43 | DOI | MR

[9] A. M. Kytmanov, E. K. Myshkina, “On power sums of roots of systems of entire functions of finite order of growth”, Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 14:3 (2014), 62–82 (in Russian)

[10] M. Passare, A. Tsikh, “Residue integrals and their Mellin transforms”, Can. J. Math., 47:5 (1995), 1037–1050 | DOI | MR

[11] E. K. Myshkina, “On One Condition for the Decomposition of an Entire Function into an Infinite Product”, Journal of Siberian Federal University, Mathematics and Physics, 7:1 (2013), 91–94

[12] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and series, Translated from the Russian by N. M. Queen, v. 2, Special functions, Second edition, Gordon Breach Science Publishers, New York, 1988 | MR

[13] I. S. Gradstein, I. M. Ryzhik, Tables of integrals, sums, series and products, Fizmatgis, M., 1963 (in Russian) | MR