On \(q\)-Hausdorff matrices (Q449570)

Ordinary Hausdorff matrices were introduced in 1917 by W. A. Hurwitz and L. L. Silverman to be the class of lower triangular matrices that commute with the Cesàro matrix of order one. F. Hausdorff (1921) reexamined this class, and developed many properties of the matrices that now bear his name. The \(q\)-Hausdorff matrices are defined similarly in terms of symbols of \(q\)-mathematics. The authors consider \(q\)-analogues of the Cesàro matrix of order one for both \(q\) in \((0,1)\) and for \(q\) greater than 1, and deduce lower bounds for these matrices.