Let us consider a distribution c with is the sum of another distribution, ω, and a linear combination of Dirac distribution with masses A 1, …, A q at the points a 1, …, a q . We have proposed a method ( in “IMACS Transaction on Orthogonal Polynomials and Their Applications” ( C. Brezinski, L. Gori, and A. Ronveaux, Eds.), pp. 365–372, Baltzer, Basel, 1991) to compute the points a 1, …, a q when ω has an asymptotic property when applied to a given sequence of orthogonal polynomials. This paper is devoted to the computation of the masses A 1, …, A q with the aid of Chebyshev polynomials, Christoffel function and ε-algorithm according to the distribution ω. An application to finding the limit of totally monotonic sequence is also given.