The purpose of this paper is to give, through the second degree character, new characterizations of a part of the family of quasi-symmetric forms. In fact, thanks to the Stieltjes function and also the moments, we give necessary and sufficient conditions for a regular form to be at the same time of the second degree, quasi-symmetric and semiclassical one of class two. We focus our attention not only on the link between all these forms and the Jacobi forms \({{\mathcal {T}}}_{p, q}={{\mathcal {J}}}(p-1/2, q-1/2), \; p, q\in {\mathbb {Z}},~p+q\ge 0\) but also on their connection with the Tchebychev form of the first kind \({{\mathcal {T}}}={\mathcal J}\left( -1/2, -1/2\right) \). The paper concludes by explicitly giving their characteristic elements of the structure relation and of the second order differential equation, which leads to interesting electrostatic models.

本文的目的是通过二阶特征给出准对称形式族的一部分的新特征。事实上，由于 Stieltjes 函数和矩，我们给出了正则形式同时是二阶、准对称和半经典二阶形式的充要条件。我们不仅将注意力集中在所有这些形式与雅可比形式之间的联系上\({{\mathcal {T}}}_{p, q}={{\mathcal {J}}}(p-1/2 , q-1/2), \; p, q\in {\mathbb {Z}},~p+q\ge 0\)以及它们与第一类切比雪夫形式的联系\({{\ mathcal {T}}}={\mathcal J}\left( -1/2, -1/2\right) \). 论文最后明确给出了它们的结构关系和二阶微分方程的特征元素，这导致了有趣的静电模型。