{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:59:31Z","timestamp":1759147171126,"version":"3.40.5"},"reference-count":20,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T00:00:00Z","timestamp":1601251200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KO 1737\/6\u20101"],"award-info":[{"award-number":["KO 1737\/6\u20101"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular G\u00f6del's functional interpretation, which we use to establish quantitative versions of both of these\u00a0results.<\/jats:p>","DOI":"10.1002\/malq.201900076","type":"journal-article","created":{"date-parts":[[2020,9,29]],"date-time":"2020-09-29T06:32:20Z","timestamp":1601361140000},"page":"300-310","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A note on the finitization of Abelian and Tauberian theorems"],"prefix":"10.1002","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2541-4678","authenticated-orcid":false,"given":"Thomas","family":"Powell","sequence":"first","affiliation":[{"name":"Department of Mathematics Technische Universit\u00e4t Darmstadt Schlossgartenstra\u00dfe 7, 64289 Darmstadt Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2020,9,28]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80020-7"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129509990351"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2010.0471"},{"key":"e_1_2_8_5_1","first-page":"233","volume-title":"Computer Science Logic, 25th International Workshop\/20th Annual Conference of the EACSL, CSL 2011","author":"Escard\u00f3 M.","year":"2011"},{"issue":"1","key":"e_1_2_8_6_1","doi-asserted-by":"crossref","first-page":"355","DOI":"10.2178\/jsl\/1264433926","article-title":"On Tao's \u201cfinitary\u201d infinite pigeonhole principle","volume":"75","author":"Gaspar J.","year":"2010","journal-title":"J. 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