Integrals with a large parameter: Hilbert transforms

Abstract

AbstractA simple and elegant method of treating one-sided Hilbert transformshas recently been described by Wong (7). This method immediately gives the form of the expansion but some of the coefficients in the expansion are in an inconvenient form for either analytical or numerical calculation. In the present paper it is shown that these coefficients can be readily determined when the Mellin transform of f(t) is known. The case is treated as an example.