2015/04/25 by Man Kam Kwong, Kwong, Man Kam
Mathematics · #26D05 #42A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26D05 #msc:42A05
paper · pdf · doi:10.48550/arxiv.1504.06705
arxiv created 2015/04/25 · arxiv updated 2015/04/28
Recently the author established an improvement of the classical Vietoris sine inequality to include sine polynomials with non-monotone coefficients. In this paper two further improvements are presented admitting sine polynomials with non-monotone and non-decaying coefficients. The extremal sums of the two results have the coefficient sequences 2a, a, 4/3, 1, 6/5, 1, 8/7, 1, ..., where a = 0.78265..., and 3, 3/2, 7/3, 7/4, 11/5, 11/6, ....