Reducing Exponential sinc Inequalities to Polynomial Inequalities in Real Analysis
A proof technique that converts hard exponential inequalities involving the sinc function into equivalent polynomial inequalities that can be verified by root-finding. Taking logarithms turns the exponential form into a product, and truncated power series expansions of ln(sin x / x), ln cos x and ln(1 ± x) — with two-sided bounds guaranteed by a non-negative-coefficient series lemma — give a polynomial that is a sufficient lower or upper bound. A student learns how to pick the truncation orders and split the interval so the resulting polynomial has a provable sign on each piece.
A new method for proving some inequalities related to several special functions
This arxiv paper by Lutovac, Malesevic, and Rasajski presents a methodological approach to proving exponential inequalities involving special functions, specifically the sinc function. The paper uses…