Sech-weight orthogonal polynomials and the finite Hilbert transform
The finite Hilbert transform generates a complete orthonormal set on [−1,1] with respect to the Chebyshev weight. We explore the potential of this set for solving finite Hilbert transform equations. By changing variables, the set becomes equivalent to polynomials orthogonal with respect to the sech weight on the real line. We also provide a brief review of the various theoretical contexts in which these orthogonal polynomials have historically appeared.