  Ruscheweyh and Salinas showed in 2004 the relationship of a celebrated
theorem of Vietoris (1958) about the positivity of certain sine and cosine sums
with the function theoretic concept of stable holomorphic functions in the unit
disc. The present paper shows that the coefficient sequence in Vietoris'
theorem is identical with the number sequence that characterizes generalized
Appell sequences of homogeneous Clifford holomorphic polynomials in
$\mathbb{R}^3.$ The paper studies one-parameter generalizations of Vietoris'
number sequence, their properties as well as their role in the framework of
Hypercomplex Function Theory.
