Summability methods and moment sequences. I. (Q1563230)

The author defines and investigates various properties of the class of infinite matrices that now bears his name. He shows that the Cesáro matrices of order \(\alpha\), the Hölder matrices, and the Euler matrices are Hausdorff matrices. He shows that the Cesáro and Hölder matrices of the same order are equivalent by introducing Hölder matrices of arbitrary order and noting that \(H^{\alpha +\beta} = H^{\alpha}H^{\beta}\). He observes the identity \((n + 1)h_{nk} = (n - k + 1)h_{n+1, k} + (k + 1)h_{n+1, k+1}\), and solves the classical moment problem.