N.I. Bazenkov - Ph.D. (Eng.) (Tomsk)
A.M. Zabolotsky - Postdoctoral Student, Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics (Tomsk). E-mail: zabolotsky_am@mail.ru

The order of expansion for expression (u1+u2+?+uk)n, where index of power n is any positive integer, while number of terms is however large, but finite, is considered. The obtained formula permits to perform the complete expansion of the expression and reveals regularities in structure of the expansion terms. Modified polynomial formula is derived, which permits complete expansion of the expression on the base of widely known relations of combinatorial mathematics (combinations and permutations). The formula gives complete presentation about structure and number of expansion terms. Investigation of regularities in structure of the expression is performed consequently during the formula derivation, which is ensuring the full clearance of the analysis. Because of raising the polynomial to the power is the typical procedure for analysis of the nonlinear circuits and systems on the multiple excitations, this paper may be useful for specialists analyzing the effects of nonlinear conversion of different nature excitations in various nonlinear systems and media, including electromagnetic compatibility community.

 

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