The spectrum of Jacobi matrices in terms of its associated weight function

Using the so-called Lanczos procedure of orthogonalization a method is developed to calculate the elements of a N-dimensional Jacobi matrix and/or the coefficients of the three-term recurrence relation of a system of orthogonal polynomials {P_m(x), m = 0, 1, 2, ?, N} in terms of the moments μ_r^′(1) of its associated weight function. The eigenvalue density ?^(N)(x) and its asymptotical limit, i.e. when N tends to infinite, are also calculated in terms of μ_r^′(1). The method is used to determine the functions ?^(N)(x) and ?(x) for some known weight functions, like the normal distribution, the uniform distribution, the semicircular distribution and the gamma or Pearson type III distribution. As a byproduct the asymptotical density of zeros of Chebyshev, Legendre and generalized Laguerre polynomials are found.