| 关于sum from n=1 to ∞(1/n~2=π~2/6)的证明及应用 |
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| 引用本文： | 刘爱春,祁根锁.关于sum from n=1 to ∞(1/n~2=π~2/6)的证明及应用[J].大学数学,2014(2):102-107. |
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| 作者姓名： | 刘爱春 祁根锁 |
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| 作者单位： | 呼和浩特民族学院数学系,呼和浩特010051 |
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| 摘 要： | 鉴于欧拉求得的无穷级数∑∞n=11n2收敛于π26的特殊性和重要性,用列举与对比的方法又给出了∑∞n=11n2=π26的若干不同的证明方法及其应用.
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| 关 键 词： | 逐项积分 傅立叶级数 逐项求和 |
On the Proof and Application of ∞∑n=1 n^2/1=6/π^2 |
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| LIUAi-chun,QI Gen-suo.On the Proof and Application of ∞∑n=1 n^2/1=6/π^2[J].College Mathematics,2014(2):102-107. |
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| Authors: | LIUAi-chun QI Gen-suo |
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| Institution: | (Department of Mathematics, H uhhot University for Nationalities, Huhhot 010051, China) |
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| Abstract: | Considering the special importance of the eqution ∞∑n=1 n^2/1=6/π^2 which is proved first by Euler, this paper will present and introduce several different proofs and applications of ∞∑n=1 n^2/1=6/π^2 by the way of listing and contrast. |
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| Keywords: | itemized integral Fourier series~ series summation |
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