Identities on Extended Catalan Numbers and Their q-Analogs

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• 作者：Roberta R. Zhou ; Wenchang Chu
• 关键词：Catalan numbers ; Hagen–Rothe formulae ; Hypergeometric series
• 刊名：Graphs and Combinatorics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：32
• 期：5
• 页码：2183-2197
• 全文大小：438 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Engineering Design
  
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：32

文摘

The Gauss and Pfaff–Saalschütz theorems on classical hypergeometric series are employed to extend the summation formulae on Catalan numbers due to Jonah, Koshy and Touchard. Their q-analogs are also investigated by means of basic hypergeometric series.