4 citations · 12 across the 7 of their papers we have counts for
6 papers · 1 filter
Centralizers of the Riordan Group
Tian-Xiao He, Yuanziyi Zhang
In this paper, we discuss centralizers in the Riordan group. We will see that Faà di Bruno's formula is an application of the Fundamental Theorem of Riordan arrays. Then the compos…
One-pth Riordan Arrays in the Construction of Identities
Tian-Xiao He
For an integer we construct vertical and horizontal one-pth Riordan arrays from a Riordan array. When , one-pth Riordan arrays reduced to well known half Riordan arr…
-sequences, -sequence, and -sequences of Riordan Matrices
Tian-Xiao He
We defined two type -sequences of Riordan arrays and present the -sequence characterization and -sequence characterization of the Riordan matrices with two type -sequen…
Duals of Bernoulli Numbers and Polynomials and Euler Number and Polynomials
Tian-Xiao He, Jinze Zheng
A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a un…
Use Impulse Response Sequences in the Construction of Number Sequence Identities
Tian-Xiao He
We define impulse response sequence in the set of all linear recurring sequences satisfying a linear recurrence relation of order . The generating function and expression of the…
Generalized Stirling Numbers and Generalized Stirling Functions
Tian-Xiao He
Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, -Gamma fun…