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In the article solution of the problem of extremal value of x(τ) is presented, for the n-th order linear systems. The extremum of x(τ) is considered as a function of the roots s 1 , s 2 , ... s n of the characteristic equation. The obtained results give a possibility of decomposition of the whole n-th order system into a set of 2-nd order systems.

Abstract. It is proved that there exist the relations between coefficients of the transcendental equations and the infinite number of their roots, similar to Vieta's formulae.These relations may be obtained for the entire analytic functions using theorems of residues and argument principle. In particular the meromorphic functions will be considered.

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