REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

  1. Repozytorium Uniwersytetu w Białymstoku
  2. Czasopisma naukowe / Journals
  3. Formalized Mathematics
  4. Formalized Mathematics, 2018, Volume 26, Issue 1

Szukanie zaawansowane
  • Zespoły i Kolekcje


  • Zaloguj się
  • Zarejestruj się
  • Mój RUB
  • FAQ
  • Polityka
  • Regulamin
  • DOI
  • Instrukcja
  • Aspekty prawne
  • Open Access
  • Archiwum


  • Kontakt
  • O Dspace
  • Strona Biblioteki
  • Strona Uczelni



    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/6834
    Pełny rekord metadanych
    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2018-08-20T06:41:52Z-
    dc.date.available2018-08-20T06:41:52Z-
    dc.date.issued2018-
    dc.identifier.citationFormalized Mathematics, Volume 26, Issue 1, Pages 69–79-
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/6834-
    dc.description.abstractIn the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits log-log growth. We introduce some auxiliary notions as harmonic numbers, telescoping series, and prove some standard properties of logarithms and exponents absent in the Mizar Mathematical Library. At the end we proceed with square-free and square-containing parts of a natural number and reciprocals of corresponding products.-
    dc.language.isoen-
    dc.publisherDeGruyter Open-
    dc.subjectprime factorization-
    dc.subjectsequence of prime reciprocals-
    dc.subjectharmonic number-
    dc.titleSequences of Prime Reciprocals. Preliminaries-
    dc.typeArticle-
    dc.identifier.doi10.2478/forma-2018-0006-
    dc.description.AffiliationInstitute of Informatics, University of Białystok, Poland-
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.-
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from ℝ to ℝ and integrability for continuous functions. Formalized Mathematics, 9(2):281–284, 2001.-
    dc.description.referencesNoboru Endou, Yasunari Shidama, and Masahiko Yamazaki. Integrability and the integral of partial functions from ℝ into ℝ. Formalized Mathematics, 14(4):207–212, 2006. doi:10.2478/v10037-006-0023-y.-
    dc.description.referencesLeonhard Euler. Variae observationes circa series infinitas. Commentarii Academiae Scientiarum Petropolitanae, 9:160–188, 1737.-
    dc.description.referencesAdam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.-
    dc.description.referencesAdam Grabowski and Christoph Schwarzweller. Revisions as an essential tool to maintain mathematical repositories. In M. Kauers, M. Kerber, R. Miner, and W. Windsteiger, editors, Towards Mechanized Mathematical Assistants. Lecture Notes in Computer Science, volume 4573, pages 235–249. Springer: Berlin, Heidelberg, 2007.-
    dc.description.referencesArtur Korniłowicz and Karol Pąk. Basel problem – preliminaries. Formalized Mathematics, 25(2):141–147, 2017. doi:10.1515/forma-2017-0013.-
    dc.description.referencesArtur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179–186, 2004.-
    dc.description.referencesRobert Milewski. Natural numbers. Formalized Mathematics, 7(1):19–22, 1998.-
    dc.description.referencesAkira Nishino and Yasunari Shidama. The Maclaurin expansions. Formalized Mathematics, 13(3):421–425, 2005.-
    dc.description.referencesKarol Pąk and Artur Korniłowicz. Basel problem. Formalized Mathematics, 25(2):149–155, 2017. doi:10.1515/forma-2017-0014.-
    dc.identifier.eissn1898-9934-
    dc.description.volume26-
    dc.description.issue1-
    dc.description.firstpage69-
    dc.description.lastpage79-
    dc.identifier.citation2Formalized Mathematics-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2018, Volume 26, Issue 1

    Pliki w tej pozycji:
    Plik Opis RozmiarFormat 
    forma-2018-0006.pdf283,7 kBAdobe PDFOtwórz
    Pokaż uproszczony widok rekordu Zobacz statystyki


    Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons