Discrete Hilbert-Type Inequalities

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Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral ...
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Improvements of Euler -Maclaurin’s Summation Formula: Preliminary Theorems

Pp. 14-26 (13)

Bicheng Yang


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.


Guangzhou, Guangdong, P. R. China