Leibniz Series forπ

Karol Pąk. "Leibniz Series forπ." Formalized Mathematics 24.4 (2016): 275-280. <http://eudml.org/doc/287991>.

@article{KarolPąk2016,
abstract = {In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. \[\{\pi \over 4\} = \sum \limits \_\{n = 0\}^\infty \{\{\{\left( \{ - 1\} \right)^n \} \over \{2 \cdot n + 1\}\}.\} \] 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/.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
keywords = {π approximation; Leibniz theorem; Leibniz series; approximation},
language = {eng},
number = {4},
pages = {275-280},
title = {Leibniz Series forπ},
url = {http://eudml.org/doc/287991},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Karol Pąk
TI - Leibniz Series forπ
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 4
SP - 275
EP - 280
AB - In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. \[{\pi \over 4} = \sum \limits _{n = 0}^\infty {{{\left( { - 1} \right)^n } \over {2 \cdot n + 1}}.} \] 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/.
LA - eng
KW - π approximation; Leibniz theorem; Leibniz series; approximation
UR - http://eudml.org/doc/287991
ER -