The natural algorithmic approach of mixed trigonometric-polynomial problems

Journal of Inequalities and Applications

Tatjana Lutovac¹  Branko Malešević¹  Cristinel Mortici² 

[1] Faculty of Electrical Engineering, University of Belgrade;Valahia University of Târgovişte;

关键词: mixed trigonometric-polynomial functions;    Taylor series;    approximations;    inequalities;    algorithms;    automated theorem proving;   

DOI  :  10.1186/s13660-017-1392-1

来源: DOAJ

【 摘 要 】

Abstract The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form ∑ i = 1 n α i x p i cos q i x sin r i x > 0 $$\sum_{i=1}^{n}\alpha _{i}x^{p_{i}} \cos ^{q_{i}} x\sin ^{r_{i}} x>0 $$ by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new rational (Padé) approximations of the function cos2 x and to improve a class of inequalities by Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.

【 授权许可】

Unknown