  In this work we deduce explicit formulae for the elements of the matrices
that represent the action of integro-differential operators over the
coefficients of generalized Fourier series. Our formulae are obtained by
performing operations on the bases of orthogonal polynomials and result
directly from the three-term recurrence relation satisfied by the polynomials.
Moreover we give exact formulae for the coefficients for some families of
orthogonal polynomials. Some tests are given to demonstrate the robustness of
the formulas presented.
