Geodesic
The solution of algebraic equations of continuous fractions of Nikiports
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 4, pp. 533-547

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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: infinite Toeplitz determinant, $r/\varphi$-algorithm, diverging continuous fractions.
Mots-clés : algebraic equation 
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Vladimir I. Shmoylov; Gennadiy A. Kirichenko. The solution of algebraic equations of continuous fractions of Nikiports. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 4, pp. 533-547. http://geodesic.mathdoc.fr/item/JSFU_2014_7_4_a11/