A Hilbert inequality and an Euler-Maclaurin summation formula

ANZIAM J. 48 (2007), 419-431

A Hilbert inequality and an Euler-Maclaurin summation formula

Mario Krnic
Department of Mathematics
University of Zagreb
Bijenicka cesta 30
10000 Zagreb
Croatia
krnic@math.hr

and

Josip Pecaric
Faculty of Textile Technology
University of Zagreb
Pierottijeva 6
10000 Zagreb
Croatia
pecaric@hazu.hr

Abstract

We obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions.

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