P分之一Riordan矩阵及恒等式构造
One-\$p\$th Riordan Arrays in the Construction of Identities

DOI：10.3770/j.issn:2095-2651.2021.02.001

 作者 单位 何天晓 Illinois Wesleyan University 数学系

本文构造了垂直和水平P分之一Riordan矩阵,这里P是大于或等于二的整数.当P等于二时,垂直和水平P分之一Riordan矩阵就是垂直和水平的半Riordan矩阵. 我们还给出了垂直和水平P分之一Riordan矩阵的A序列的生成函数.垂直和水平P分之一Riordan矩阵可以用来发现许多恒等式,并简化许多著名恒等式的证明.

For an integer \$p\geq 2\$ we construct vertical and horizontal one-\$p\$th Riordan arrays from a Riordan array. When \$p=2\$ one-\$p\$th Riordan arrays are reduced to well known half Riordan arrays. The generating functions of the \$A\$-sequences of vertical and horizontal one-\$p\$th Riordan arrays are found. The vertical and horizontal one-\$p\$th Riordan arrays provide an approach to construct many identities. They can also be used to verify some well known identities readily.