Hilbert transforms and sum rules of Bessel moments

Abstract

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we verify and generalize two conjectures by Bailey–Borwein–Broadhurst–Glasser and Broadhurst–Mellit.