MathDB
Miklós Schweitzer 1956- Problem 9

Source:

October 11, 2015
college contests

Problem Statement

9. Show that if the trigonometric polynomial f(θ)=∑v=1navcos⁡vθf(\theta)= \sum_{v=1}^{n} a_v \cos v\theta monotonically decreases over the closed interval [0,π][0,\pi], then the trigonometric polynomial g(θ)=∑v=1navsin⁡vθg(\theta)=\sum_{v=1}^{n}a_v \sin v\theta is non negative in the same interval. (S. 26)
Back to ProblemsView on AoPS