On a Pair of Hyperstandard Reciprocal Relations with Applications
Received:October 19, 2012  Revised:February 19, 2013
Key Words: difference operator   hyper-real field   zero-monad   Riemann-Liouville integral   M\"{o}bius-type inversion   reciprocal relation.  
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Author NameAffiliation
Leetsch C. HSU 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.02.003
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