Improvements of Euler -Maclaurin’s Summation Formula: Preliminary Theorems
Pp. 14-26 (13)
In this chapter, for optimizing the methods of est imating the series and weight coefficients, we introduce
some preliminary theorems of improving Euler-Maclaurin’ s summation formula. A few useful corollaries and
inequalities are considered. By the way of applications, some new inequalities on Hurwitz ζ-function restricted in the
real axis are given.
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