An Expression for the Remainder Terra of the Euler-Maclaurin Summation Formula
Received:October 10, 1980  
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Hsu L.C. Jilin University 
Wang Xinghua Hangzhou University 
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Abstract:
      Let f(t) be a functiin defined on [a,b] and Let f(r-1)(t)(r≥2) be of bounded variation there. Then for any x∈[0,l] we have (?).It is shown that the expression given above has various consequences including those mentioned in [1], [2],[3], respectively. Also the result included in this note is a refined estimate fcr the remainder term of an asymptotic expansion of a kind of oscillatory integral (See (13) - (16)).
Citation:
DOI:10.3770/j.issn:1000-341X.1981.01.012
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