| 一类无穷级数和的计算方法 |
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| 引用本文： | 邱为钢.一类无穷级数和的计算方法[J].安庆师范学院学报(自然科学版),2007,13(2):74-75. |
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| 作者姓名： | 邱为钢 |
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| 作者单位： | 湖州师范学院,理学院,浙江,湖州,313000 |
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| 基金项目： | 国家自然科学基金项目资助(10547116) |
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| 摘 要： | 雅可比椭圆函数具有双周期性质,可以展开为傅里叶级数,也可以展开为幂级数,对比变量的展开系数,得到了一类无穷求和的解析表达式。Einstein级数具有模变换性质,可以得到无穷求和的恒等式,取模参数为特殊值,就得到了另一类无穷求和的值。
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| 关 键 词： | 无穷成和 椭圆函数 Einstein级数 |
| 文章编号： | 1007-4260（2007）02-0074-02 |
| 修稿时间： | 2006-08-05 |
The computational way for one Class of Infinite Series |
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| QIU Wei-Gang.The computational way for one Class of Infinite Series[J].Journal of Anqing Teachers College(Natural Science Edition),2007,13(2):74-75. |
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| Authors: | QIU Wei-Gang |
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| Institution: | School of Science, Huzhou Teachers College, Huzhou 313000 , China |
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| Abstract: | Jacobi elliptic function has the property of two periods and it can be expanded into Fourier series and power series as well.Comparing the coefficient of the two kinds of series,some analyzed formulas are derived in solving infinite sum.An identity of another infinite sum is derived from modular transform property of Einstein series.Its value is got as the modulus takes some special values. |
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| Keywords: | Infinite sum Elliptic function Einstein series |
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