Horizontal and vertical formulas for exponential Riordan matrices and their applications

Cheon, Gi Sang and Jung, Ji Hwan and Barry, Paul (2018) Horizontal and vertical formulas for exponential Riordan matrices and their applications. Linear Algebra and Its Applications, 541. pp. 266-284. ISSN 0024-3795

Full text not available from this repository. (Request a copy)

Abstract

In this paper, we show that an infinite lower triangular matrix A=[aij]i,j∈N0 is an exponential Riordan matrix A=E(g,f) given by ∑i≥jaijzi/i!=gfj/j! if and only if there exist both a horizontal pair {hn;h˜n}n≥0 and a vertical pair {vn;v˜n}n≥0 of sequences that represent all the elements in the matrix. As a consequence, we obtain that if the horizontal and vertical pairs of an exponential Riordan matrix are identical then the matrix is an involution. In addition, this concept can be applied to obtain the determinants of the production matrix and some conditions for the d-orthogonality of the Sheffer polynomial sequences.

Item Type:	Article
Additional Information:	Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2016R1A5A1008055) and the Ministry of Education (NRF-2016R1A6A3A11930452). Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( 2016R1A5A1008055 ) and the Ministry of Education ( NRF-2016R1A6A3A11930452 ). Publisher Copyright: © 2017
Uncontrolled Keywords:	/dk/atira/pure/subjectarea/asjc/2600/2602
Departments or Groups:
Depositing User:	Admin SSL
Date Deposited:	19 Oct 2022 23:06
Last Modified:	07 Jun 2023 18:43
URI:	http://repository-testing.wit.ie/id/eprint/4036

Actions (login required)

View Item