Abstract
changes its sign an infinite number of times. The aim of the present paper is to prove an improvement of this theorem. It shall be proved that the total curvature of the polygonal line having the vertices n+i log Pn (n = 1, 2, 3, ***) in the complex z-plane is infinite. This implies that Pnu?lPn-1 -p2 changes its sign an infinite number of times, but our result also contains some quantitative information regarding the oscillations of the sequence Pn+IPPn-lp.2 The total curvature G of a finite polygonal line situated in the complex z-plane may be defined as follows:
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