Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices

Abstract

In this paper, we present a new analogue of the Filbert and Lilbert matrices whose indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formul ae are derived for the LU-decompositions, their inverses and the inverse of the main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.