\(q\)-Triplicate inverse series relations with applications to \(q\)-series
type: Item
instance of: scholarly article
title: \(q\)-Triplicate inverse series relations with applications to \(q\)-series
zbMATH Open document ID: 1087.33008
author: Yusen Zhang
author: Wei Chen
published in: Rocky Mountain Journal of Mathematics
publication date: 2006-01-24T00:00:00Z
review text: Inverse relations were investigated in depth in [\textit{J. Riordan}, An introduction to combinatorial analysis. Wiley (1958; Zbl 0078.00805)]. A special case is the identities of \textit{H. W. Gould} and \textit{L. C. Hsu} [``Some new inverse series relations'', Duke Math J. 40, 885--891 (1973; Zbl 0281.05008)], and its \(q\)-analogue [\textit{L. Carlitz}, ``Some inverse relations'', Duke Math J. 40, 893--901 (1973; Zbl 0276.05012)]. The paper under review treats a \(q\)-triplicate inverse relation in the spirit of Carlitz [loc. cit.], which is a \(q\)-analogue of papers by Chu. Various special cases of this inverse relation are studied, however the reviewer is uncertain about the validity of formulas 2.10-12, 2.14-16 and later formulas. Anyway the matrix inverse relation is very interesting.
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5001013
zbMATH Keywords: matrix inverse relation
zbMATH Keywords: very-well-poised \(q\)-series
zbMATH Keywords: Gould-Hsu inversion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069692
OpenAlex ID: W2093109938
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DOI: 10.1216/RMJM/1181069692
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description: scientific article; zbMATH DE number 5001013