Lemniscate elliptic functions: Difference between revisions

Revision as of 21:56, 19 June 2025

Revision as of 22:02, 19 June 2025

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* {{cite book |last1= Houzel |first1=Christian |author-link1=Christian Houzel |date=1978 |chapter=Fonctions elliptiques et intégrales abéliennes |trans-chapter=Elliptic functions and Abelian integrals |editor-last=Dieudonné |editor-first= Jean |editor-link1=Jean Dieudonné |title= Abrégé d'histoire des mathématiques, 1700–1900. II |publisher=Hermann |pages=1–113 |language=fr}}

* {{cite journal |last1=Hyde |first1=Trevor |year=2014 |title=A Wallis product on clovers |journal=The American Mathematical Monthly |volume=121 |issue=3 |pages=237–243 |url=https://math.uchicago.edu/~tghyde/Hyde%20--%20A%20Wallis%20product%20on%20clovers.pdf |doi=10.4169/amer.math.monthly.121.03.237 }}

* {{cite journal |last1=Kubota |first1=Tomio |authorlink1=Tomio Kubota |date=1964 |title=Some arithmetical applications of an elliptic function |journal=Crelle's Journal |volume='''214'''/'''215''' |pages=141–145 |doi=10.1515/crll.1964.214-215.141 }}

* {{cite journal |last1=Langer |first1=Joel C. |first2=David A. |last2=Singer |year=2010 |title=Reflections on the Lemniscate of Bernoulli: The Forty-Eight Faces of a Mathematical Gem |journal=Milan Journal of Mathematics |volume=78 |issue=2 |pages=643–682 |url=https://case.edu/artsci/math/langer/jlpreprints/fortyeight2010.pdf |doi=10.1007/s00032-010-0124-5 }}

* {{cite journal |last1=Langer |first1=Joel C. |first2=David A. |last2=Singer |year=2011 |title=The lemniscatic chessboard |journal=Forum Geometricorum |volume=11 |pages=183–199 |url=https://forumgeom.fau.edu/FG2011volume11/FG201119index.html }}

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| title = Conformal Projections Based on Elliptic Functions

| ___location = Toronto | publisher = B. V. Gutsell, York University

| series = ''Cartographica Monographs'' | volume = 16

| url = https://archive.org/details/conformalproject0000leel | url-access = limited

| isbn = 0-919870-16-3

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* {{Cite book |last1=Lemmermeyer |first1=Franz |title=Reciprocity Laws: From Euler to Eisenstein |publisher=Springer |year=2000 |isbn=3-540-66957-4}}

* {{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=10.23071080/2764197600029890.2006.11920331 |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 }}

* {{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/ }}

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* {{cite journal |last1=Neuman |first1=Edward |authorlink1=Edward Neuman |year=2007 |title=On Gauss lemniscate functions and lemniscatic mean |journal=Mathematica Pannonica |volume=18 |issue=1 |pages=77–94 |url=http://mathematica-pannonica.ttk.pte.hu/articles/mp18-1/MP18-1(2007)pp077-094.pdf }}

* {{cite journal |last1=Nishimura |first1=Ryo |title=New properties of the lemniscate function and its transformation |journal=Journal of Mathematical Analysis and Applications |date=2015 |volume=427 |issue=1 |pages=460–468 |doi=10.1016/j.jmaa.2015.02.066 |doi-access=free }}

* {{cite journal |last1=Ogawa |first1=Takuma |title=Similarities between the trigonometric function and the lemniscate function from arithmetic view point |journal=Tsukuba Journal of Mathematics |date=2005 |volume=29 |issue=1 |doi=10.21099/tkbjm/1496164894 |urldoi-access=https://projecteuclid.org/journals/tsukuba-journal-of-mathematics/volume-29/issue-1/Similarities-between-the-trigonometric-function-and-the-lemniscate-function-from/10.21099/tkbjm/1496164894.fullfree }}

* {{cite journal |last1=Peirce |first1=Charles Sanders |authorlink1=Charles Sanders Peirce |date=1879 |title=A Quincuncial Projection of the Sphere |journal=American Journal of Mathematics |volume=2 |issue=4 |pages=394–397 |doi=10.2307/2369491 |doi-access=free |jstor=2369491 |jstor-access=free |url=https://archive.org/details/sim_american-journal-of-mathematics_1879_2/page/n403/mode/2up}}

* {{cite book |last=Popescu-Pampu |first=Patrick |date=2016 |title=What is the Genus? |series=Lecture Notes in Mathematics |volume=2162 |publisher=Springer |doi=10.1007/978-3-319-42312-8 |isbn=978-3-319-42311-1 }}

* {{cite book |last1=Prasolov |first1=Viktor |last2=Solovyev |first2=Yuri |date=1997 |chapter=4. Abel's Theorem on Division of Lemniscate |title=Elliptic functions and elliptic integrals |series=Translations of Mathematical Monographs |volume=170 |publisher=American Mathematical Society. |doi=10.1090/mmono/170 |isbn=978-0-8218-0587-9 }}

* {{cite journal| last1=Rančić |first1=Miodrag |last2=Purser |first2=R. James | last3=Mesinger |first3=Fedor |date=1996 |title=A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates |journal=Quarterly Journal of the Royal Meteorological Society |volume=122 |issue=532 |pages=959–982 |doi=10.1002/qj.49712253209 |bibcode=<!-- useless bibcode 1996QJRMS.122..959R --> }}

* {{cite book |last1=Reinhardt |first1=William P. |last2=Walker |first2=Peter L. |year=2010a |display-editors=1 |editor1-last=Olver |editor1-first=Frank |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=22. Jacobian Elliptic Functions |chapter-url=https://dlmf.nist.gov/22 |title-link=Digital Library of Mathematical Functions }}

* {{cite book |last1=Reinhardt |first1=William P. |last2=Walker |first2=Peter L. |year=2010b |display-editors=1 |editor1-last=Olver |editor1-first=Frank |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=23. Weierstrass Elliptic and Modular Functions |chapter-url=https://dlmf.nist.gov/23 |title-link=Digital Library of Mathematical Functions }}

* {{cite arXiv |last1=Robinson |first1=Paul L. |title=The Lemniscatic Functions |date=2019a |eprint=1902.08614 |class=math.CV}}

* {{cite arXiv |last1=Robinson |first1=Paul L. |title= The Elliptic Functions in a First-Order System |date=2019b |eprint=1903.07147 |class=math.CV}}

* {{cite journal |last1=Rosen |first1=Michael |authorlink1=Michael Rosen (mathematician) |title=Abel's Theorem on the Lemniscate |journal=The American Mathematical Monthly |date=1981 |volume=88 |issue=6 |pages=387–395 |doi=10.23071080/232182100029890.1981.11995279 |jstor=2321821 }}

* {{cite book |last1=Roy |first1=Ranjan |title=Elliptic and Modular Functions from Gauss to Dedekind to Hecke |publisher=Cambridge University Press |page=28 |year=2017 |isbn=978-1-107-15938-9}}

* {{cite book |chapter=Some milestones of lemniscatomy |last1=Schappacher |first1=Norbert |author-link1=Norbert Schappacher | date= 1997 |editor1-last=Sertöz |editor1-first=S. |title=Algebraic Geometry |type=Proceedings of Bilkent Summer School, August 7–19, 1995, Ankara, Turkey |publisher=Marcel Dekker |pages=257–290 | chapter-url=http://irma.math.unistra.fr/~schappa/NSch/Publications_files/1997_LemniscProvis.pdf}}