In condensed-matter physics, the density of eigenstates n(E) of hermitian operators is often computed using continued-fraction expansions of the Hilbert transform of n(E). The framework of this technique is briefly reviewed in the present paper. Emphasis is given on the generalized-moments method, intimately related to orthogonal polynomials. The generalized-moments method allows the continued-fraction coefficients to be computed using well-conditionned algorithms. Averaged densities of states can be determined by this method, which interpolates continuously between the power moments method and the Lanezos tridiagonalization algorithm. The problem of convolution of n(E) is also considered.