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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we prove the $q$-analogue of the fundamental theorem of Riordan arrays.
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Key Findings & Data:In particular, by defining two new binary operations $\ast_{q} $ and $\ast _{1/q}$, we obtain a $q$-analogue of the Riordan representation of the $q$-Pascal matrix.
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Conclusion & Impact:In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riordan representation · Pascal matrices · $q$-calculus
Abstract
In this paper, we prove the $q$-analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations $\ast_{q} $ and $\ast _{1/q}$, we obtain a $q$-analogue of the Riordan representation of the $q$-Pascal matrix. In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.
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Cite This Article
TUĞLU, N., YEŞİL, F., DZIEMIANCZUK, M., KOÇER, E. G. (2016). $q$-Riordan array for $q$-Pascal matrix and its inverse matrix. Turkish Journal of Mathematics, Cilt: 40 - Sayı: 5, 1038–1048. https://ajindex.com/articles/723251