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The generalized $q$-Pilbert matrix

In: Mathematica Slovaca, vol. 64, no. 5
Emrah Kiliç - Helmut Prodinger
Rok, strany: 2014, 1083 - 1092
Kľúčové slová:
Filbert matrix, Pilbert matrix, Fibonacci numbers, $q$-analogues, LU-decomposition, Cholesky decomposition, Zeilberger's algorithm
O článku:
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.
Ako citovať:
ISO 690:
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
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