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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.  相似文献
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