| 与$zeta(2k 1)$函数有关的两类快速收敛级数 |
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| 引用本文： | 周彩莲,吴云飞. 与$zeta(2k 1)$函数有关的两类快速收敛级数[J]. 数学研究及应用, 2011, 31(3): 521-527 |
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| 作者姓名： | 周彩莲 吴云飞 |
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| 作者单位： | 宁波大学数学系, 浙江 宁波 315211;宁波大学数学系, 浙江 宁波 315211 |
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| 基金项目： | 国家自然科学基金(Grant No.10571095),宁波市自然科学基金(Grant No.2009A610078),宁波大学科研基金(Grant No.xkl09042). |
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| 摘 要： | Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.
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| 关 键 词： | Riemann zeta function rapidly convergent series. |
| 收稿时间： | 2009-10-01 |
| 修稿时间： | 2010-11-20 |
New Rapidly Convergent Series Concerning $zeta(2k 1)$ |
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| Cai Lian ZHOU and Yun Fei WU. New Rapidly Convergent Series Concerning $zeta(2k 1)$[J]. Journal of Mathematical Research with Applications, 2011, 31(3): 521-527 |
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| Authors: | Cai Lian ZHOU and Yun Fei WU |
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| Affiliation: | Department of Mathematics, Ningbo University, Zhejiang 315211, P. R. China;Department of Mathematics, Ningbo University, Zhejiang 315211, P. R. China |
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| Abstract: | Values of new series $$sum_{n=1}^{infty}frac{(2n-1)!zeta(2n)}{(2n+2k)!}alpha^{2n}, sum_{n=1}^{infty}frac{(2n-1)!zeta(2n)}{(2n+2k+1)!}beta^{2n}$$ are given concerning $zeta(2k+1)$, where $k$ is a positive integer, $alpha$ can be taken as $1$, $1/2$, $1/3$, $2/3$, $1/4$, $3/4$, $1/6$, $5/6$ and $beta$ can be taken as $1$, $1/2$. Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for $alpha = 1/3$, or $alpha = 1/4$, or $alpha = 1/6$. |
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| Keywords: | Riemann zeta function rapidly convergent series. |
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