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. [ABSTRACT FROM AUTHOR]