Leibniz Series for π

Pąk, Karol

Leibniz Series for π

Formalized Mathematics

Volume 24 (2016): Issue 4 (December 2016)

By:

Karol Pąk

Open Access

|Feb 2017

References

[1] George E. Andrews, Richard Askey, and Ranjan Roy. Special Functions. Cambridge University Press, 1999.10.1017/CBO9781107325937
Search in Google Scholar Back to article
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.
Search in Google Scholar Back to article
[3] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507–513, 1990.
Search in Google Scholar Back to article
[4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.
Search in Google Scholar Back to article
[5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.
Search in Google Scholar Back to article
[6] Lokenath Debnath. The Legacy of Leonhard Euler: A Tricentennial Tribute. World Scientific, 2010.10.1142/p698
Search in Google Scholar Back to article
[7] Noboru 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.
Search in Google Scholar Back to article
[8] Konrad Knopp. Infinite Sequences and Series. Dover Publications, 1956. ISBN 978-0-486-60153-3.
Search in Google Scholar Back to article
[9] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703–709, 1990.
Search in Google Scholar Back to article
[10] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1 (3):471–475, 1990.
Search in Google Scholar Back to article
[11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269–272, 1990.
Search in Google Scholar Back to article
[12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477–481, 1990.
Search in Google Scholar Back to article
[13] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887–890, 1990.
Search in Google Scholar Back to article
[14] Xiquan Liang and Bing Xie. Inverse trigonometric functions arctan and arccot. Formalized Mathematics, 16(2):147–158, 2008. doi:10.2478/v10037-008-0021-3.10.2478/v10037-008-0021-3
Search in Google Scholar Back to article
[15] Akira Nishino and Yasunari Shidama. The Maclaurin expansions. Formalized Mathematics, 13(3):421–425, 2005.
Search in Google Scholar Back to article
[16] Chanapat Pacharapokin, Kanchun, and Hiroshi Yamazaki. Formulas and identities of trigonometric functions. Formalized Mathematics, 12(2):139–141, 2004.
Search in Google Scholar Back to article
[17] Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125–130, 1991.
Search in Google Scholar Back to article
[18] Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213–216, 1991.
Search in Google Scholar Back to article
[19] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335–338, 1997.
Search in Google Scholar Back to article
[20] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255–263, 1998.
Search in Google Scholar Back to article

DOI: https://doi.org/10.1515/forma-2016-0023 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

Journal RSS Feed

Language: English

Page range: 275 - 280

Submitted on: Oct 18, 2016

Published on: Feb 23, 2017

Published by: University of Białystok, Department of Pedagogy and Psychology

In partnership with: Paradigm Publishing Services

Publication frequency: 1 times per year

Keywords:

Related subjects:

Computer sciences, other

© 2017 Karol Pąk, published by University of Białystok, Department of Pedagogy and Psychology
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Previous article Volume 24 (2016): Issue 4 (December 2016)Next article