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Power Series of Roots of Systems of Entire Functions of Finite Growth Order

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We find power series of roots of a system of nonalgebraic equations consisting of entire or meromorphic functions of finite growth order. Bibliography: 9 titles.

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References

  1. L. A. Ajzenberg, “On a formula of the generalized multidimensional logarithmic residue and the solution of system of nonlinear equations,” [in Russian], Dokl. Akad. Nauk SSSR 234, No. 3, 505–508 (1977); English transl.: Sov. Math. Dokl. 18, 691–695 (1977).

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  4. A. M. Kytmanov and Z. E. Potapova, “Formulas for determining power sums of roots of systems of meromorphic functions” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 8, 36–45 (2005).

  5. V. I. Bykov, A. M. Kytmanov, and S. G. Myslivets, “Power sums of nonlinear systems of equations” [in Russian], Dokl. Akad. Nauk, Ross. Akad. Nauk 416, No. 1, 7–10 (2007); English transl.: Dokl. Math. 76, No. 2, 641–644 (2007).

  6. A. A. Kytmanov, “An algorithm for calculating power sums of roots for a class of systems of nonlinear equations” [in Russian], Programmirovanie 36, No. 2, 55–63 (2010); English transl.: Program. Comput. Soft. 36, No. 2, 103–110 (2010).

  7. E. C. Titchmarsh, The Theory of Functions, Oxford Univ. Press, London (1975).

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  8. A. M. Kytmanov and E. K. Myshkina, “Evaluation of power sums of roots for systems of nonalgebraic equations in C n” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 12, 78–83 (2013); English transl.: Russ. Math. 57, No. 12, 31–43 (2013).

  9. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Vol. 1: Elementary Functions [in Russian], Nauka, Moscow (1981); English transl.: Gordon and Breach, New York (1986).

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Authors and Affiliations

  1. Siberian Federal University, 79, Svobodnyi Av., Krasnoyarsk, 660041, Russia

    A. M. Kytmanov & E. K. Myshkina

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  1. A. M. Kytmanov
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  2. E. K. Myshkina
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Correspondence to A. M. Kytmanov.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 3, 2014, pp. 62–82.

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Kytmanov, A.M., Myshkina, E.K. Power Series of Roots of Systems of Entire Functions of Finite Growth Order. J Math Sci 213, 868–886 (2016). https://doi.org/10.1007/s10958-016-2748-7

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  • DOI: https://doi.org/10.1007/s10958-016-2748-7

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