Van der Corput不等式的进一步改进
Further Improvement of Van der Corput’s Inequality
摘要: 本文首先改进对Euler常数的估计式，在胡克已改进的Van der Corput不等式的基础上进一步改进Van der Corput不等式，得到，其中r 是Euler常数，,。
Abstract: On the basis of Hu Ke’s result, by reforming the estimate inequality of Euler constant, the improved Van der Corput’s inequality is obtained. Our result is:

where r is Euler constant, , .。

文章引用：洪静, 洪勇. Van der Corput不等式的进一步改进[J]. 理论数学, 2013, 3(1): 9-13. http://dx.doi.org/10.12677/PM.2013.31003

参考文献

[1] J. G. Ven der Corput. Generations of Carleman’s inequality. Koninklijke, Akademie Van Wetenschappen to Amsterdam, 1936, 39(8).
[2] 胡克. 关于Van der Corput 不等式[J]. 数学杂志, 2003, 23(1): 126-128.
[3] 包那. Euler常数与Euler公式[J]. 数学的实践与认识, 1988, 18(4): 55-64.
[4] B. C. Yang. Note on Hardy’s inequality. Journal of Mathematical Analysis and Applications, 1999, 234: 717-722.

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