Approximation of a weighted Hilbert transform by using perturbed Laguerre zeros

In the present paper is proposed a numerical method to approximate Hilbert transforms of the type (Formula Presented.), where w(x) = e-xxa, a >-1 is a Laguerre weight, by means of a new Lagrange interpolation process essentially based on the midpoints between two consecutive zeros of Laguerre polynomials. Theoretical error estimates are proved in some weighted uniform spaces and some numerical tests which confirm the theoretical estimates are shown.