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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 24, Issue 4 (Dec 2016)

Issues

Leibniz Series for π

Karol Pąk
  • Institute of Informatics, University of Białystok, Ciołkowskiego 1M, 15-245 Białystok, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-02-23 | DOI: https://doi.org/10.1515/forma-2016-0023

Summary

In this article we prove the Leibniz series for π which states that π4=n=0(1)n2n+1.

The formalization follows K. Knopp [8], [1] and [6]. Leibniz’s Series for Pi is item #26 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

Keywords: π approximation; Leibniz theorem; Leibniz series

MSC 2010: 40G99; 03B35

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About the article

Received: 2016-10-18

Published Online: 2017-02-23

Published in Print: 2016-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0023.

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© 2016 Karol Pąk, published by De Gruyter Open. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License. BY-SA 3.0

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