On an extension of Riordan array and its application in the construction of convolution-type and Abel-type identities

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 {p(n) (t)}, where p(n)(t) is of degree n, we extend the ordinary Riordan array (resp. Riordan group) to a generalized Riordan array (resp. generalized Riordan group) associated with {p(n)(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. (C) 2014 Elsevier Ltd. All rights reserved.