# The generalized $q$-Pilbert matrix

In: Mathematica Slovaca, vol. 64, no. 5
Emrah Kiliç - Helmut Prodinger

## Details:

Year, pages: 2014, 1083 - 1092
Keywords:
Filbert matrix, Pilbert matrix, Fibonacci numbers, $q$-analogues, LU-decomposition, Cholesky decomposition, Zeilberger's algorithm
A generalized $q$-Pilbert matrix from [KILI\c{C}, E.–PRODINGER, H.: \textit{The $q$-Pilbert matrix}, Int. J. Comput. Math. \textbf{89} (2012), 1370–1377] is further generalized, introducing one additional parameter. Explicit formul\ae are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use $q$-analysis and to leave the justification of the necessary identities to the $q$-version of Zeilberger's celebrated algorithm. However, the necessary identities have appeared already in disguised form in the paper referred above, so that no new computations are necessary.
Kiliç, E., Prodinger, H. 2014. The generalized $q$-Pilbert matrix. In Mathematica Slovaca, vol. 64, no.5, pp. 1083-1092. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0260-4
Kiliç, E., Prodinger, H. (2014). The generalized $q$-Pilbert matrix. Mathematica Slovaca, 64(5), 1083-1092. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0260-4