Geodesic
On Certain Discrete Inequalities involving Partial Sums
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 222-234

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim in this paper is to prove inequalities of the form 1 or 2 for all real values of the parameters α, β and all non-negative (in some cases all positive) xi . Obviously, an is finite in all cases, and we shall show that An is finite if α and α + β are both non-negative. In all cases, we obtain sharp values of the constants an, An (when finite), as well as bounds for these constants, and their behaviour as n → ∞. In case a < 0, we naturally consider only positive xi , otherwise the xi may be non-negative. Although we always write xi ≧ 0 in the following, this should be read as xi > 0 in case α < 0; similar remarks apply to the parameter t introduced below. 
Beesack, Paul R. On Certain Discrete Inequalities involving Partial Sums. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 222-234. doi: 10.4153/CJM-1969-022-1
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