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

Tian-Xiao He, Leetsch C. Hsu, Xing Ron Ma

Research output: Journal ArticleArticlepeer-review


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.
Original languageAmerican English
JournalEuropean Journal of Combinatorics
StatePublished - 2014


  • Formal power series
  • expansion formula
  • Riordan group
  • matrix multiplication
  • convolution formula


  • Mathematics

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