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BY-NC-ND 3.0 license Open Access Published by De Gruyter November 15, 2014

The generalized q-Pilbert matrix

Emrah Kiliç and Helmut Prodinger
From the journal Mathematica Slovaca


A generalized q-Pilbert matrix from[KILIÇ, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370–1377] is further generalized, introducing one additional parameter. Explicit formulæ 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.

[1] KILIÇ, E.— PRODINGER, H.: A generalized Filbert matrix, Fibonacci Quart. 48 (2010), 29–33. Search in Google Scholar

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[3] PRODINGER, H.: A generalization of a Filbert matrix with 3 additional parameters, Trans. Roy. Soc. South Africa 65 (2010), 169–172. in Google Scholar

[4] RICHARDSON, T.: The Filbert matrix, Fibonacci Quart. 39 (2001), 268–275. Search in Google Scholar

Published Online: 2014-11-15
Published in Print: 2014-10-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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