关于Euler-Maclaurin求和公式的一种余项表示

An Expression for the Remainder Terra of the Euler-Maclaurin Summation Formula

中文摘要:

      

英文摘要:

      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)).