| Hardy-Hilbert重级数不等式的推广与改进 |
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| 引用本文： | 洪勇. Hardy-Hilbert重级数不等式的推广与改进[J]. 数学的实践与认识, 2002, 32(5): 849-854 |
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| 作者姓名： | 洪勇 |
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| 作者单位： | 海南师范学院数学系,海南海口,571158 |
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| 摘 要： | 本文将著名的 Hardy-Hilbert重级数不等式∑∞m=1 ∑∞n=1ambnm + n≤ πsin(π/p) ∑∞n=1apn1p ∑∞n=1bqn1q∑∞m=1 ∑∞n=1anm + np ≤ πsin(π/p)p∑∞n=1apn进行了带参数形式的推广 ,同时改进了这些不等式
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| 关 键 词： | Hardy-Hilbert重级数不等式 Euler-Maclaurin求和公式 权系数 |
| 修稿时间： | 2000-10-12 |
A Extension and Improvement of Hardy-Hilbert′s Double Series Inequality |
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| HONG Yong. A Extension and Improvement of Hardy-Hilbert′s Double Series Inequality[J]. Mathematics in Practice and Theory, 2002, 32(5): 849-854 |
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| Authors: | HONG Yong |
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| Abstract: | In this paper, Hardy-Hilbert ′s double series inequalities[FC(][]∑[DD(]∞[]m=1[DD)]∑[DD(]∞[]n=1[DD)][SX(]a-mb n[]m+n[SX)] ≤[SX(]π[]sin(π/p)[SX)] [JB((]∑[DD(]∞[]n=1[DD)]ap n[JB))] [SX(]1[]p[SX)] [JB((]∑[DD(]∞[]n=1[DD)]b q n[JB))] [SX(]1[]q[SX)] =[]∑[DD(]∞[]m=1[DD)][JB((]∑[DD(]∞[]n=1[DD)][SX(]a-n[]m+n[SX)][JB))]p ≤[JB([][SX(]π[]sin(π/p)[SX)][JB)]]p∑[DD(]∞[]n=1[DD)]ap n[FC)] are generalized and refined into parameter forms. |
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| Keywords: | Hardy-Hilbert′s double series inequal ity Euler-Maclourin′s summation formula weight coefficient |
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