engleski

A Hilbert inequality and an Euler-Maclaurin summation formula

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.

inequalities; Hilbert's inequality; Bernoulli numbers; Bernoulli polynomials; Euler-Maclaurin summation formula; homogeneous function; kernel; weight function; equivalent inequalities

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