{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:11:17Z","timestamp":1783901477342,"version":"3.55.0"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In this article, using the Mizar system [2], [3], we deal with Riemann\u2019s improper integral on infinite interval [1]. As with [4], we referred to [6], which discusses improper integrals of finite values.<\/jats:p>","DOI":"10.2478\/forma-2021-0024","type":"journal-article","created":{"date-parts":[[2022,7,9]],"date-time":"2022-07-09T16:34:39Z","timestamp":1657384479000},"page":"279-294","source":"Crossref","is-referenced-by-count":5,"title":["Improper Integral. Part II"],"prefix":"10.2478","volume":"29","author":[{"given":"Noboru","family":"Endou","sequence":"first","affiliation":[{"name":"National Institute of Technology, Gifu College , 2236-2 Kamimakuwa, Motosu , Gifu , Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2022,7,9]]},"reference":[{"key":"2026071215073889095_j_forma-2021-0024_ref_001","unstructured":"[1] Tom M. Apostol. Mathematical Analysis. Addison-Wesley, 1969."},{"key":"2026071215073889095_j_forma-2021-0024_ref_002","doi-asserted-by":"crossref","unstructured":"[2] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol P\u0105k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261\u2013279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007\/978-3-319-20615-8_17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2026071215073889095_j_forma-2021-0024_ref_003","doi-asserted-by":"crossref","unstructured":"[3] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026071215073889095_j_forma-2021-0024_ref_004","doi-asserted-by":"crossref","unstructured":"[4] Noboru Endou. Improper integral. Part I. Formalized Mathematics, 29(4):201\u2013220, 2021. doi:10.2478\/forma-2021-0019.","DOI":"10.2478\/forma-2021-0019"},{"key":"2026071215073889095_j_forma-2021-0024_ref_005","doi-asserted-by":"crossref","unstructured":"[5] Noboru Endou, Yasunari Shidama, and Masahiko Yamazaki. Integrability and the integral of partial functions from \u211d into \u211d. Formalized Mathematics, 14(4):207\u2013212, 2006. doi:10.2478\/v10037-006-0023-y.","DOI":"10.2478\/v10037-006-0023-y"},{"key":"2026071215073889095_j_forma-2021-0024_ref_006","doi-asserted-by":"crossref","unstructured":"[6] Masahiko Yamazaki, Hiroshi Yamazaki, and Yasunari Shidama. Extended Riemann integral of functions of real variable and one-sided Laplace transform. Formalized Mathematics, 16(4):311\u2013317, 2008. doi:10.2478\/v10037-008-0038-7.","DOI":"10.2478\/v10037-008-0038-7"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2021-0024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T23:58:39Z","timestamp":1783900719000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2021-0024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,1]]},"references-count":6,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,7,9]]},"published-print":{"date-parts":[[2021,12,1]]}},"alternative-id":["10.2478\/forma-2021-0024"],"URL":"https:\/\/doi.org\/10.2478\/forma-2021-0024","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,1]]}}}