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Journal of Siberian Federal University. Mathematics & Physics, 2014, Volume 7, Issue 4, Pages 533–547 (Mi jsfu398)  
The solution of algebraic equations of continuous fractions of Nikiports

Vladimir I. Shmoylova, Gennadiy A. Kirichenkob

a Southern Scientific Center of RAS, Chehova, 41, Rostov-on-Don, 344006, Russia
b Southern Federal University, ITA, Nekrasovsky, 44, Taganrog, Rostov region, 347928, Russia
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Abstract: Analytical expressions representing all the roots of a random algebraic equation of $n$-th degree in terms of the equation coefficients are presented in the paper. These formulas consist of two ratios of infinite Toeplitz determinants. The diagonal elements of the determinants are the coefficients of algebraic equations. To find complex roots the method of summation of divergent continued fractions is used.
Keywords: algebraic equation, infinite Toeplitz determinant, $r/\varphi$-algorithm, diverging continuous fractions.
Received: 06.04.2014
Received in revised form: 06.07.2014
Accepted: 06.08.2014
Document Type: Article
UDC: 517.524
Language: English
Citation: Vladimir I. Shmoylov, Gennadiy A. Kirichenko, “The solution of algebraic equations of continuous fractions of Nikiports”, J. Sib. Fed. Univ. Math. Phys., 7:4 (2014), 533–547
Citation in format AMSBIB
\Bibitem{ShmKir14}
\by Vladimir~I.~Shmoylov, Gennadiy~A.~Kirichenko
\paper The solution of algebraic equations of continuous fractions of Nikiports
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 4
\pages 533--547
\mathnet{http://mi.mathnet.ru/jsfu398}
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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