| 关于一般Hilbert二重级数定理的改进 |
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| 引用本文： | 杨必成. 关于一般Hilbert二重级数定理的改进[J]. 数学研究, 1996, 29(2): 64-70 |
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| 作者姓名： | 杨必成 |
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| 作者单位： | 广东教育学院数学系 |
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| 摘 要： | 应用Ｅｌｕｅｒ求和公式．证明对任意正整数ｎ及实数ｐ＞１．有这里，由此改进了一般Ｈｉｌｂｅｒｔ二重级数定理．
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| 关 键 词： | Hilbert不等式，Euler求和公式，Bernoulli数 |
A Refinement on The General Hilbert''s Double Series Theorem |
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| Yang Bicheng. A Refinement on The General Hilbert''s Double Series Theorem[J]. Journal of Mathematical Study, 1996, 29(2): 64-70 |
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| Authors: | Yang Bicheng |
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| Affiliation: | Department of Math. Guang Dong College of Education |
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| Abstract: | In this paper,using Euler's summation formula,we prove the following inequality where p>1,:and n is an arbitrary positive integer,andUsing this result,we give a refinement on The General Hibert's Double Series Theorem, which is the Hilbert Inequality extended by Hardy-Riesz. |
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| Keywords: | Hilbert Inequality Euler's summation formula Bernoulli numbers |
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