Horizontal and vertical formulas for exponential Riordan matrices and their applications

Gi Sang Cheon, Ji Hwan Jung, Paul Barry

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)266-284
Number of pages19
JournalLinear Algebra and Its Applications
Publication statusPublished - 15 Mar 2018


  • d-orthogonal polynomials
  • Exponential Riordan matrix
  • Production matrix
  • Sheffer sequence


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