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Absolute convergence — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Absolute_convergence
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T08:32:07.721Z
SHA-256 of the archived text: bd50df0ddf176f08afc9c9717fd154adbe35cac6c9db3cc924438e6ace9e1d62
Stable URL of this page: https://metraipolis.com/documento/dc_da47bf336dba

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Absolute convergence — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Absolute_convergence (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_da47bf336dba (Metraipolis archive dc_da47bf336dba, sha256 bd50df0ddf176f08afc9c9717fd154adbe35cac6c9db3cc924438e6ace9e1d62)

BibTeX

@misc{dcda47bf336dba,
  title = {Absolute convergence — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Absolute_convergence},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_da47bf336dba; sha256 bd50df0ddf176f08afc9c9717fd154adbe35cac6c9db3cc924438e6ace9e1d62},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Absolute_convergence. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ∑n=0∞an is said to converge absolutely if ∑n=0∞|an|=L for some real number L. Similarly, an improper integral of a function, ∫0∞f(x)dx, is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if ∫0∞|f(x)|dx=L. A convergent series that is not absolutely convergent is called conditionally convergent. Absolute convergence is important for the study of infinite series, because its definition guarantees that a series will have some "nice" behaviors of finite sums that not all convergent series possess. For instance, rearrangements do not change the value of the sum, which is not necessarily true for conditionally convergent series.

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Absolute convergence» — https://en.wikipedia.org/wiki/Absolute_convergence
Wikidata Q332465: «a property of infinite series» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q332465
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Absolute_convergence?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1308904187, consultata il 2026-11-07T08:25:33.598Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d1d82a49a3ac8c85fc00816cd9fe64bb8b8cea13145b3b52594e47c147c17e3c