| 一对超标准互反关系及应用 |
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| 引用本文： | 徐利治.一对超标准互反关系及应用[J].数学研究及应用,2013,33(2):155-163. |
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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学院, 辽宁 大连 116024 |
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| 摘 要： | The method of non-standard analysis(NSA) is used to construct a pair of hyperstandard reciprocal formulas involving certain non-standard difference operators with realnumber orders.Our main result consists of some extensions of earlier results appearing previously 5].An essential meaning of the paper is to indicate the fact that only the basic idea of NSA is applicable to the construction of a unified pattern that may have certain applications to both the analysis and the number theory.
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| 关 键 词： | difference operator hyper-real field zero-monad Riemann-Liouville integral Mo¨bius-type inversion reciprocal relation. |
| 收稿时间： | 2012/10/19 0:00:00 |
| 修稿时间： | 2013/2/19 0:00:00 |
On a Pair of Hyperstandard Reciprocal Relations with Applications |
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| Leetsch C. HSU.On a Pair of Hyperstandard Reciprocal Relations with Applications[J].Journal of Mathematical Research with Applications,2013,33(2):155-163. |
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| Authors: | Leetsch C HSU |
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| Institution: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P.R.China |
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| Abstract: | The method of non-standard analysis (NSA) is used to construct a pair of hyperstandard reciprocal formulas involving certain non-standard difference operators with real-number orders. Our main result consists of some extensions of earlier results appearing previously 5]. An essential meaning of the paper is to indicate the fact that only the basic idea of NSA is applicable to the construction of a unified pattern that may have certain applications to both the analysis and the number theory. |
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| Keywords: | difference operator hyper-real field zero-monad Riemann-Liouville integral M\"{o}bius-type inversion reciprocal relation |
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