Approximating the finite Hilbert transform via a companion of Ostrowski's inequality for function of bounded variation and applications

The finite Hilbert transform plays an important role in scientific and engineering computing. By using a companion of Ostrowski's inequality for function of bounded variation, we give some new approximations of the finite Hilbert transform, which may have the better error bounds than the known results obtained via Ostrowski type inequality. Some numerical experiments are also presented.