| 关于一种高阶算术几何级数的求和问题 |
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| 引用本文： | 徐利治.关于一种高阶算术几何级数的求和问题[J].吉首大学学报(自然科学版),1996,17(3):1-5. |
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| 作者姓名： | 徐利治 |
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| 作者单位： | 大连理工大学数学科学研究所!中国大连，116024 |
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| 基金项目： | 国家自然科学基金!组合数学重点项目 |
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| 摘 要： | 本文对形如的高阶算术几何级数研究了显式求和公式的构造问题，并给出了公式系列的速归生成法则。作为例子，对一类多项式系数的三角和计算提供了求和公式。
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| 关 键 词： | 第二类Stirling数 高阶零差 递归关系 |
On a Problem of Summing a Kind of Higher-Order Arithmetic-Geometric Progression |
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| Xu Lizhi.On a Problem of Summing a Kind of Higher-Order Arithmetic-Geometric Progression[J].Journal of Jishou University(Natural Science Edition),1996,17(3):1-5. |
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| Authors: | Xu Lizhi |
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| Abstract: | Let a be a real or complex number with and . Denote by S(p,j) the Stirlingnumber of the second kind,and by niop the j -th difference of S(p,j). this note presents a straight forward derivation of an explicit summation formula ofthe formwhere pis any given positive integer. Consequently,a pair of summation formulas are given ofthe trigonometric sums cos and sin,where f(x) is a polynomial in x ofdegree p with real confficients and f(O) = being real with .Also expounded isa recursive process for the construction of the sequence of formulas for 1, 2,3, ... |
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| Keywords: | The Second Kind of Stirling Number Higher Degnee Zero-Crossing Recurrence Relation |
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