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:
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.