Lemniscate elliptic functions: Difference between revisions

Revision as of 23:09, 19 June 2025

Revision as of 23:11, 19 June 2025

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* {{cite book |last1=Bottazzini |first1=Umberto |authorlink1=Umberto Bottazzini |last2=Gray |first2=Jeremy |authorlink2=Jeremy Gray |date=2013 |title=Hidden Harmony – Geometric Fantasies: The Rise of Complex Function Theory |publisher=Springer |doi=10.1007/978-1-4614-5725-1 |isbn=978-1-4614-5724-4 }}

* {{cite book |last=Carlson |first=Billie C. |year=2010 |authorlink1=Bille C. Carlson |display-editors=1 |editor1-last=Olver |editor1-first=Frank |editor1-link=Frank W. J. Olver |editor2-last=Lozier |editor2-first=Daniel |editor3-last=Boisvert |editor3-first=Ronald |editor4-last=Clark |editor4-first=Charles |title=NIST Handbook of Mathematical Functions |publisher=Cambridge |chapter=19. Elliptic Integrals |chapter-url=https://dlmf.nist.gov/19 |title-link=Digital Library of Mathematical Functions }}

* {{cite journal |last=Cox |first=David Archibald |authorlink1=David A. Cox |date=January 1984 |title=The Arithmetic-Geometric Mean of Gauss |url=https://www.researchgate.net/publication/248675540 |journal=L'Enseignement Mathématique |volume=30 |issue=2 |pages=275–330 }}

* {{cite journal |last1=Cox |first1=David Archibald |last2=Shurman |first2=Jerry |date=2005 |title=Geometry and number theory on clovers |journal=The American Mathematical Monthly |volume=112 |issue=8 |pages=682–704 |doi=10.1080/00029890.2005.11920241 |url=https://people.reed.edu/~jerry/Clover/cloverexcerpt.pdf }}

* {{cite book |last1=Cox |first1=David Archibald |year=2012 |chapter=The Lemniscate |pages=463–514 |title=Galois Theory |publisher=Wiley |doi=10.1002/9781118218457.ch15 |isbn=978-1-118-07205-9 }}

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* {{cite tech report |last1=Levien |first1=Raph |year=2008 |authorlink1=Raph Levien |title=The elastica: a mathematical history |number=UCB/EECS-2008-103 |institution=University of California at Berkeley |url=https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-103.pdf}}

* {{cite journal |last1=Levin |first1=Aaron |title=A Geometric Interpretation of an Infinite Product for the Lemniscate Constant |journal=The American Mathematical Monthly |date=2006 |volume=113 |issue=6 |pages=510–520 |doi=10.1080/00029890.2006.11920331 |jstor=27641976 |url=https://web.archive.org/web/20041220213524id_/http://math.berkeley.edu:80/~adlevin/Lemniscate.pdf }}

* {{cite journal |last1=Lindqvist |first1=Peter |last2=Peetre |first2=Jaak |authorlink2=Jaak Peetre |title=Two Remarkable Identities, Called Twos, for Inverses to Some Abelian Integrals |journal=The American Mathematical Monthly |date=2001 |volume=108 |issue=5 |pages=403–410 |doi=10.1080/00029890.2001.11919766 |url=https://people.math.osu.edu/lang.162/book/LiPe3.pdf |archive-url=https://web.archive.org/web/20220528124044/https://people.math.osu.edu/lang.162/book/LiPe3.pdf |archive-date=28 May 2022-05-28 }}

* {{cite book |last1=Markushevich |first1=Aleksei Ivanovich |authorlink1=Aleksei Ivanovich Markushevich |title=The Remarkable Sine Functions |date= 1966 |publisher=Elsevier |url=https://archive.org/details/markushevich-the-remarkable-sine-functions/ }}

* {{cite book |last1=Markushevich |first1=Aleksei Ivanovich |title=Introduction to the Classical Theory of Abelian Functions |series=Translations of Mathematical Monographs |date=1992 |volume=96 |publisher=American Mathematical Society |doi=10.1090/mmono/096 |isbn=978-0-8218-4164-8 }}