A method to evaluate the Hilbert transform on (0,  +∞)

The author proposes a method to approximate the Hilbert transform on the real positive semiaxis by a suitable Lagrange interpolating polynomial. The method employs truncated Gaussian rules and uses the interlacing properties of the zeros of generalized Laguerre polynomials. The error estimate in a weighted uniform norm is proved and some numerical tests show the efficacy of the proposed procedure.

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