On Shapiro's Catalan convolution

DOI10.1016/j.aam.2010.07.003zbMath1227.05029OpenAlexW2086622194MaRDI QIDQ534174

George E. Andrews

Publication date: 17 May 2011

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2010.07.003

zbMATH Keywords

\(q\)-hypergeometric seriesCatalan numbersShapiro convolution

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Exponential and trigonometric functions (33B10)

Related Items (7)

Convolution identities involving the central binomial coefficients and Catalan numbers ⋮ Proof of Andrews' conjecture on a₄φ₃summation ⋮ A bijective proof of Shapiro's Catalan convolution ⋮ Two matrix inversions associated with the Hagen-Rothe formula, their \(q\)-analogues and applications ⋮ A combinatorial proof of Shapiro's Catalan convolution ⋮ Further identities on Catalan numbers ⋮ Full \(q\)-analogue for an identity of \(\lambda\)-extended Catalan numbers

Cites Work

• Catalan numbers, \(q\)-Catalan numbers and hypergeometric series
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On Shapiro's Catalan convolution