Factorization of the Hilbert Matrix Based on Cesàro and Gamma Matrices

In this paper, we introduce a factorization for the infinite Hilbert matrix based on Cesaro matrices. Moreover, through the relation between Cesaro and Gamma matrices, we extract our second factorization for the Hilbert matrix based on Gamma matrices. The results of these factorizations are two new inequalities one of which is a generalized version of the well-known Hilbert’s inequality.