On an Extension of Riordan Array and its Application in the Construction of Convolution-type and Abel-type Identities

Authors

Tian-Xiao He, Illinois Wesleyan UniversityFollow
Leetsch Hsu, Dalian University of Technology
Xing Ron Ma, Soochow University

Publication Date

January 2014

Comments

The is published by Elsevier, http://www.sciencedirect.com/science/article/pii/S0195669814000821.

Abstract

Using the basic fact that any formal power series over the real or complex number field can always be expressed in terms of given polynomials {pn(t)}{pn(t)}, where pn(t)pn(t) is of degree nn, we extend the ordinary Riordan array (resp. Riordan group) to a generalized Riordan array (resp. generalized Riordan group) associated with {pn(t)}{pn(t)}. As new application of the latter, a rather general Vandermonde-type convolution formula and certain of its particular forms are presented. The construction of the Abel type identities using the generalized Riordan arrays is also discussed.

Disciplines

Mathematics

Recommended Citation

He, Tian-Xiao; Hsu, Leetsch; and Ma, Xing Ron, "On an Extension of Riordan Array and its Application in the Construction of Convolution-type and Abel-type Identities" (2014). Scholarship. 13.
https://digitalcommons.iwu.edu/math_scholarship/13