On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles

2017/08/04 by Wolfdieter Lang, Lang, Wolfdieter
Mathematics · #05A15 #11B83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Secondary 11B37

paper · pdf · doi:10.48550/arxiv.1708.01421

openalex publication_date 2017/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous computation for general Riordan number triangles leads to a formula for the logarithmic generating function of the ordinary generating functions of the product of the entries of the diagonal sequence of Pascal's triangle and those of the Riordan triangle. For some examples these ordinary generating functions yield in both cases coefficient triangles of certain numerator polynomials.

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