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  "body": "\n## Summary\n\nHausdorff summation is a family of [[matrix summability methods|M6311DWJ1E]], one for each sequence $(\\mu_n)$ of numbers.\nThe matrix is built from $(\\mu_n)$ and its iterated differences with binomial weights.\nThe family contains the [[Cesàro|N8ZGG7EW6J]] methods and the [[Euler|81Q4ERP594]] methods as special cases.\nHausdorff characterized the regular methods of the family by a moment condition on $(\\mu_n)$, which links summability with the Hausdorff moment problem.\n\n## Explanations\n\n### L1 human\n\nMany classical summation methods turn a sequence into weighted averages with binomial coefficients in the weights.\nHausdorff noticed that they all come from one recipe fed with a sequence $(\\mu_n)$.\nFeeding $\\mu_n = \\frac{1}{n+1}$ into the recipe gives the plain running averages of Cesàro.\nFeeding $\\mu_n = 2^{-n}$ gives Euler's averages with the weights of Pascal's triangle.\n",
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