Residue integrals and Waring’s formulas for algebraic or even transcendental systems

References

• Van der Waerden BL . Modern algebra. New York (NY): Frederick Unger Publishing Co.; 1950.
   Google Scholar
• Buchberger B . Gröbner bases, an algorithmic method in polynomial ideal theory. In: Bose NK , editor. Multidimensional systems theory. Dordrecht: Reidel; 1985. p. 184–232.
   Google Scholar
• Adams WW , Loustaunau P . An introduction to Gröbner bases. Vol. 3, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 1994.
   Google Scholar
• Aizenberg LA . On a formula of the gereralized multidimensional logarithmic residue and the solution of system of nonlinear equations. Sov Math Doc. 1977;18:691–695.
   Google Scholar
• Aizenberg LA , Yuzhakov AP . Integral representations and residues in multidimensional complex analysis. Translations of mathematical monographs. Providence (RI): American Mathematical Society; 1983.
   Google Scholar
• Tsikh AK . Multidimensional residues and their applications. Vol. 103, Translations of mathematical monographs. Providence (RI): American Mathematical Society; 1992.
   Google Scholar
• Bykov V , Kytmanov A , Lazman M , Passare M , editors. Elimination methods in polynomial computer algebra. Vol. 448, Mathematics and applications. Dordreht: Kluwer Academic Publishers; 1998.
   Google Scholar
• Bykov VI . Modeling of the critical phenomena in chemical kinetics. Moscow: Komkniga; 2006. Russian.
   Google Scholar
• Bykov VI , Tsybenova SB . Non-linear models of chemical kinetics. Moscow: Krasand; 2011. Russian.
   Google Scholar
• Kulikov VR , Stepanenko VA . On solutions and Waring’s formulas for systems of n algebraic equations for n unknowns. St Petersburg Math J. 2015;26(5):839–848.
   Web of Science ®Google Scholar
• Kytmanov AM , Potapova ZE . Formulas for determining power sums of roots of systems of meromorphic functions. Izvestiya VUZ Mat. 2005;49(8):36–45. Russian.
   Google Scholar
• Bykov VI , Kytmanov AM , Myslivets SG . Power sums of nonlinear systems of equations. Docl Math. 2007;76(2):641–645.
   Google Scholar
• Kytmanov AA . Analogs of recurrent Newton formulas. Russ Math. 2009;53(10):34–44.
   Google Scholar
• Kytmanov AM , Myshkina EK . Evaluation of power sums of roots for systems of non-algebraic equations in ℂ n . Russ Math. 2013;57(12):31–43.
   Google Scholar
• Kytmanov AA , Kytmanov AM , Myshkina EK . Finding residue integrals for systems of non-algebraic equations in ℂ n . J Symb Comput. 2015;66:98–110.
   Web of Science ®Google Scholar
• Kytmanov AM , Myshkina EK . On calculation of power sums of roots one class of systems non-algebraic equations. Siberian Electron Math Rep. 2015;12:190–209. Russian.
   Google Scholar
• Kytmanov AM , Myshkina EK . Power series of roots of systems of entire functions of finite growth order. J Math Sci (US). 2016;213(6):868–886.
   Google Scholar
• Kytmanov AM , Khodos OV . On systems of non-algebraic equation in ℂ n . 1st USA-Uzbekistan Conference on Analysis and Mathematical Physics, California State Univ, Fullerton, CA, May 20-23, 2014. In: Topics in several complex variables, Contemporary Mathematics, 2016. Vol. 662, p. 77–88.
   Google Scholar
• Kytmanov AA . An algorithm for calculating power sums of roots for a class of systems of nonlinear equations. Program Comput Soft. 2010;36(2):103–110.
   Web of Science ®Google Scholar
• Khodos OV . On some systems of non-algebraic equations in ℂ n . J Siberian Federal Univ -- Math Phys. 2014;7(4):455–465.
   Google Scholar
• Tsikh AK . The Bezout theorem in the space of theory functions. On the solution of a system of algebraic equations. Nekotorye voprosy mnogomernogo kompleksnogo analiza. Krasnoyarsk: Institut fiziki SO AN SSSR; 1980. p. 185–196. Russian.
   Google Scholar
• Passare M , Tsikh A . Residue integrals and their Melin transforms. Can J Math. 1995;47(5):1037–1050.
   Web of Science ®Google Scholar
• Lelong P , Gruman L . Entire functions of several complex variables. Berlin: Springer-Verlag; 1986.
   Google Scholar
• Myshkina EK . On one condition for the decomposition of an entire function into an infinite product. J Siberian Federal Univ -- Math Phys. 2014;7(1):91–94.
   Google Scholar
• Prudnikov AP , Brychkov YuA , Marichev OI . Integrals and series. Vol. 1, Elementary functions. Translated from the Russian and with a preface by Queen NM. New York (NY): Gordon & Breach Science Publishers; 1986.
   Google Scholar