  We show that the skew-growth function of a dual Artin monoid of finite type P
has exactly rank(P) =: l simple real zeros on the interval (0, 1]. The proofs
for types A_l and B_l are based on an unexpected fact that the skew-growth
functions, up to a trivial factor, are expressed by Jacobi polynomials due to a
Rodrigues type formula in the theory of orthogonal polynomials. The skew-growth
functions for type D_l also satisfy Rodrigues type formulae, but the relation
with Jacobi polynomials is not straightforward, and the proof is intricate. We
show that the smallest root converges to zero as the rank l of all the above
types tend to infinity.
