Extremal polynomials for the Rogosinski--Szegő estimates of the third coefficient of nonnegative sine polynomials

Dmitriy Dmitrishin, Alexander Stokolos, Walter Trebels

In the class of normalized sine-polynomials $S(t),$ non-negative on $[0,\pi ],$ W.Rogosinski and G.Szegő 1950 considered a number of extremal problems and proved, among other things,…