标题： 关于广义维多利亚数列——起源、性质和应用 显示英文标题

标题： On generalized Vietoris' number sequences - origins, properties and applications

摘要： Ruscheweyh 和 Salinas 在 2004 年展示了 Vietoris（1958）关于某些正弦和余弦和的正性的一个著名定理与单位圆内稳定全纯函数的函数理论概念之间的关系。 本文表明 Vietoris 定理中的系数序列与表征在$\mathbb{R}^3.$中的广义 Appell 序列的数列相同。本文研究了 Vietoris 数列的一参数推广，它们的性质以及它们在超复函数理论框架中的作用。 显示英文摘要

摘要： 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.