Discrete Hilbert-Type Inequalities

Improvements of Euler -Maclaurin’s Summation Formula: Preliminary Theorems

Author(s): Bicheng Yang

Pp: 14-26 (13)

Doi: 10.2174/978160805242411101010014

* (Excluding Mailing and Handling)

Abstract

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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