\(q\)-Triplicate inverse series relations with applications to \(q\)-series (Q812508)

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.