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  "body": "\n## Summary\n\nA Riesz mean of a series $\\sum a_n$ is a weighted partial sum in which the term $a_n$ is damped by a factor $(1 - \\lambda_n/\\omega)^{\\delta}$.\nHere $\\lambda_n$ is a given increasing sequence and $\\omega$ is a cut-off that grows to infinity.\nThe series is Riesz summable when these means converge.\nWith $\\lambda_n = n$ and $\\delta = 1$ the Riesz means at integer cut-offs are the [[Cesàro means|08R2V9GZF7]] of the partial sums.\nRiesz means with $\\lambda_n = \\ln n$ are a standard tool for [[Dirichlet series|8MWTEF6462]] in analytic number theory.\n\n## Explanations\n\n### L1 human\n\nA partial sum cuts a series off sharply: terms before the cut-off count fully and the rest not at all.\nA Riesz mean cuts it off smoothly: terms well before the cut-off count almost fully, and terms near it count only a little.\nThe smooth cut-off removes much of the oscillation that makes a series diverge.\nThe parameter $\\delta$ controls how smooth the cut-off is.\n",
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