Investigation of asymptotic properties of roots of large absolute value of quasi-polynomials
Abstract
The present paper investigates the distribution of large absolute value roots of quasi-polynomials of the form (1) (see article). As a result of the research it is shown that in the presence of the principal term the function (1) has two groups of large modulo roots with negative real parts, and the roots of each group obey the asymptotic dependences established in the work of the author [1]. The questions touched upon in the paper belong to the general problem of investigating the distribution of roots of quasi-polynomials, to which, as is known, many practical problems related to the construction and study of transients in linear systems with distributed parameters and with delay lead.
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References
- Labazin V.G. Some properties of large in absolute value roots of transcendental equations. Vestnik Leningradskogo universiteta, 1953, No. 11. (in Russian)
- Markushevich A.I. Theory of analytic functions. Gostekhizdat, 1950. (in Russian)
- Chebotarev N.G. and Meiman N.N. The Raus-Gurwitz problem for polynomials and integer functions. Trudy matem. in-ta im. V. A. Steklova, 1949, vol. XXVI. (in Russian)