P分之一Riordan矩阵及恒等式构造

One-$p$th Riordan Arrays in the Construction of Identities

中文关键词:  Riordan矩阵  P分之一Riordan矩阵  A序列  生成函数  恒等式

英文关键词:Riordan array  one-$p$th Riordan arrays  $A$-sequence  generating function  identities

中文摘要:

      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.

英文摘要:

      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.