P.J.D. Blancas and E.A. Galapon, “Finite-part integration of the Hilbert transform,” https://arxiv.org/abs/2210.14462
This is a major revision of the original preprint. The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms—the first is an infinite series of finite-part of divergent integrals, and the… Read More »