Hausdorff summation

Summary

Hausdorff summation is a family of matrix summability methods, one for each sequence $(\mu_n)$ of numbers. The matrix is built from $(\mu_n)$ and its iterated differences with binomial weights. The family contains the Cesàro methods and the Euler methods as special cases. Hausdorff characterized the regular methods of the family by a moment condition on $(\mu_n)$, which links summability with the Hausdorff moment problem.