On an inequality of Horst Alzer
β Scribed by Malcolm T. McGregor
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 146 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0019-3577
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A generalization of Alzer's inequality is proved. It is shown that this inequality is satisfied for a large class of increasing convex sequences.
Using the mathematical induction and Cauchy's mean-value theorem, for any , where n and m are natural numbers, k is a nonnegative integer. The lower bound is best w possible. This inequality generalizes the Alzer's inequality J. Math. Anal. Appl. 179 Ε½ . x 1993 , 396α402 . An open problem is prop
We prove: Let n>O be an integer. Then we have for all real numbers r >O: where both bounds are best possible. The right-hand side of (\*) refines an inequality of Bennett.