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

ASYMMETRIC GENERALIZATIONS OF THE FILBERT MATRIX AND VARIANTSEmrah Kilic, Helmut ProdingerDepartment of Mathematics, TOBB University of Economics and Technology, Ankara, Turkey; Department of Mathematics, University of Stellenbosch, Stellenbosch, South AfricaAbstract: Four generalizations of the Filbert matrix are considered, with additional asymmetric parameter settings. Explicit formulae are derived for the LUdecompositions, 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 Full text of the article: (for faster download, first choose a mirror)
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