Geodesic
Asymmetric Generalizations of the Filbert Matrix and Variants
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 267 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Four generalizations of the Filbert matrix are considered, with additional asymmetric parameter settings. Explicit formule 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 : 11B39 05A30 15A23 
@article{PIM_2014_N_S_95_109_a21,
     author = {Emrah K{\i}l{\i}\c{c} and Helmut Prodinger},
     title = {Asymmetric {Generalizations} of the {Filbert} {Matrix} and {Variants}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {267 },
     publisher = {mathdoc},
     volume = {_N_S_95},
     number = {109},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a21/}
}
TY  - JOUR
AU  - Emrah Kılıç
AU  - Helmut Prodinger
TI  - Asymmetric Generalizations of the Filbert Matrix and Variants
JO  - Publications de l'Institut Mathématique
PY  - 2014
SP  - 267 
VL  - _N_S_95
IS  - 109
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a21/
LA  - en
ID  - PIM_2014_N_S_95_109_a21
ER  - 
%0 Journal Article
%A Emrah Kılıç
%A Helmut Prodinger
%T Asymmetric Generalizations of the Filbert Matrix and Variants
%J Publications de l'Institut Mathématique
%D 2014
%P 267 
%V _N_S_95
%N 109
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a21/
%G en
%F PIM_2014_N_S_95_109_a21
Emrah Kılıç; Helmut Prodinger. Asymmetric Generalizations of the Filbert Matrix and Variants. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 267 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a21/