论文标题
Borel三角形和Borel多项式的特征
Characterizations of the Borel triangle and Borel polynomials
论文作者
论文摘要
我们使用Riordan阵列理论来赋予Borel三角形及其相关的多项式序列的特征。我们表明，Borel多项式是一个正交多项式家族的矩序列，其系数阵列是Riordan阵列。检查了加泰罗尼亚矩阵在定义borel三角形中的作用。我们将Borel三角形概括为两个参数三角形的家族。生成功能表示为雅各比持续的分数以及适当的二次表达式的零。 Borel三角形作为矩阵的Hadamard产品。我们研究了研究的三角形的逆转。我们介绍了大惊小怪的三角形和大惊小怪的三角形的概念。我们以加泰罗尼亚三角形的一些评论结尾。
We use Riordan array theory to give characterizations of the Borel triangle and its associated polynomial sequence. We show that the Borel polynomials are the moment sequence for a family of orthogonal polynomials whose coefficient array is a Riordan array. The role of the Catalan matrix in defining the Borel triangle is examined. We generalize the Borel triangle to a family of two parameter triangles. Generating functions are expressed as Jacobi continued fractions, as well as the zeros of appropriate quadratic expressions. The Borel triangle is exhibited as a Hadamard product of matrices. We investigate the reversions of the triangles studied. We introduce the notion of Fuss-Borel triangles and Fuss-Catalan triangles. We end with some remarks on the Catalan triangle.
