A symbolic treatment of Riordan arrays |
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| Authors: | José Agapito Ângela Mestre Pasquale Petrullo Maria M Torres |
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| Institution: | 1. Centro de Estruturas Lineares e Combinatórias, Universidade de Lisboa, Portugal;2. Universitá degli studi della Basilicata, Potenza, Italy |
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| Abstract: | We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel?s identity for polynomials. In particular, we obtain a novel non-recursive formula for Riordan arrays and derive, from this new formula, some known recurrences and a new recurrence relation for Riordan arrays. |
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| Keywords: | Riordan arrays Umbral calculus Abel?s identity |
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