Explicit inversion of cosh-weighted Finite Hilbert Transform

Several identities of the cosh-weighted finite Hilbert Transform and the Bertola-Katsevich-Tovbis inversion formulas are rederived by the Sokhotski-Plemelj formula and the Poincare-Bertrand formula. The explicit formulas are derived for the cosh-weighted Hilbert transform of the exponential Chebyshev functions. Numerical experiments are performed to study the computational effects of the inversion formulas.