  In this paper, the asymptotic formulas for Eulerian numbers, refined Eulerian
numbers and the coefficients of descent polynomials are obtained directly from
the spline interpretations of these numbers. Having related these numbers
directly to B-splines [15], we can take advantage of many powerful spline
techniques to derive various results of these numbers. The asymptotic formulas
for the Eulerian numbers Ad;k agree with the previously known results which
were given by L. Carlitz et al.(1972)[2] and S.Tanny (1973) [18], but the
convergence order is much better. We also give the asymptotic representations
of refined Eulerian numbers which is in terms of the Hermite polynomials.
