A New Family of Nonnegative Sine Polynomials

Abstract

We present a new family of sine polynomials that are nonnegative for all $x$ in $[0,\pi ]$. We also characterize all nonnegative sine polynomials of degree 3 and all nonnegative cosine polynomials of degree 2. In the latest version, typos in (1.4) and (1.6) are corrected (with >= replaced by <=).

References in corpus (4)

• Nonnegative Trigonometric Polynomials, Sturms Theorem, and Symbolic Computation
• Sturm Theorem and a Refinement of Vietoris Inequality for Cosine Polynomials
• Improved Vietoris Sine Inequalities for Non-Monotone, Non-Decaying Coefficients
• Nonnegative Trigonometric Polynomials and Sturms Theorem