| 一类调和级数的递推求和公式 |
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| 引用本文： | 李向阳,方成.一类调和级数的递推求和公式[J].工科数学,2012(5):129-132. |
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| 作者姓名： | 李向阳 方成 |
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| 作者单位： | [1]安徽师范大学数学计算机科学学院,芜湖241000 [2]浙江财经学院数学与统计学院,杭州310018 |
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| 摘 要： | 通过对一个周期函数进行傅里叶级数展开，得到了偶数阶的调和级数以及交错的奇数阶调和级数求和的递推公式，然后在此基础之上，得到了其他两类调和级数的递推求和公式。
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| 关 键 词： | 调和级数 递推公式 傅里叶级数 无限和 Mathematica |
Recursive Summation Formulas for Harmonic Series |
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| LI Xiang-yang,FANG Cheng.Recursive Summation Formulas for Harmonic Series[J].Journal of Mathematics For Technology,2012(5):129-132. |
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| Authors: | LI Xiang-yang FANG Cheng |
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| Institution: | 1. School of Math. and Computer Sci. , Anhui Normal Univ. , Wuhu 241000,China; 2. School of Math. and Statistic, Zhejiang Univ. of Finance - Econ. , Hangzhou 310018,China) |
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| Abstract: | We develop a recursive formula for even order harmonic series and one for alternating odd order harmonic series by an application of Fourier series expansion of a periodic function with the help of mathematical software-Mathematica 7. And then for the other two kinds of harmonic series, we get similar results derived from the previous ones. |
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| Keywords: | harmonic series recursive formula Fourier series infinite sum mathematica |
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