EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 95[109], pp. 267–280 (2014)

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ASYMMETRIC GENERALIZATIONS OF THE FILBERT MATRIX AND VARIANTS

Emrah Kilic, Helmut Prodinger

Department of Mathematics, TOBB University of Economics and Technology, Ankara, Turkey; Department of Mathematics, University of Stellenbosch, Stellenbosch, South Africa

Abstract: Four generalizations of the Filbert matrix are considered, with additional asymmetric parameter settings. Explicit formulae are derived for the LU-decompositions, their inverses, and the inverse matrix. The approach is mainly to use the $q$-analysis and to leave the justification of the necessary identities to the $q$-version of Zeilberger's algorithm for some of them, and for the rest of the necessary identities, to guess the relevant quantities and proving them later by induction.

Classification (MSC2000): 11B39, 05A30, 15A23

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Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.

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