About: Dixon elliptic functions

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In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane. Because these functions satisfy the identity , as real functions they parametrize the cubic Fermat curve , just as the trigonometric functions sine and cosine parametrize the unit circle .

Attributes	Values
rdfs:label	Dixon elliptic functions (en)
rdfs:comment	In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane. Because these functions satisfy the identity , as real functions they parametrize the cubic Fermat curve , just as the trigonometric functions sine and cosine parametrize the unit circle . (en)
foaf:depiction
dcterms:subject	Complex analysis
Wikipage page ID	51402829 (xsd:integer)
Wikipage revision ID	1121913630 (xsd:integer)
Link from a Wikipage to another Wikipage	Root of unity Schwarz–Christoffel mapping Meromorphic function Beta function Desmos (graphing) Hypergeometric function Regular hexagon Unit circle Doubly periodic function Jacobi elliptic functions Zeros and poles Complex plane Elliptic function Eisenstein integer Gamma function Green's theorem Conformal map Conformal map projection Lemniscate elliptic functions Stack Exchange Function of a real variable Trigonometric function Weierstrass elliptic function Lattice (group) Alfred Cardew Dixon Lee conformal world in a tetrahedron Göran Dillner Hermann Schwarz Arthur Cayley Complex analysis Abel elliptic functions Abelian integral Hexagonal tiling Fermat curve Initial value problem On-Line Encyclopedia of Integer Sequences Séminaire Lotharingien de Combinatoire Weierstrass elliptic functions dbr:Oscar_Sherman_Adams
Link from a Wikipage to an external page	https://oeis.org/A104133 https://oeis.org/A104134 https://oeis.org/A197374 https://gdz.sub.uni-goettingen.de/id/PPN599484047_0011%3Ftify= https://gdz.sub.uni-goettingen.de/id/PPN600494829_0024%3Ftify= https://dlmf.nist.gov/23.5%23v https://archive.org/details/elempropellipt00dixorich/ https://archive.org/details/novaactaregiaeso38kung/page/94/ https://archive.org/details/proceedingsofcam4188083camb/page/106/ https://arxiv.org/abs/1901.04296 https://arxiv.org/pdf/0901.1379.pdf https://arxiv.org/pdf/1608.05677 https://doi.org/10.1007/BF02038206 https://doi.org/10.1007/s00605-021-01512-0 https://doi.org/10.1179/caj.1973.10.1.22 https://link.springer.com/chapter/10.1007/978-3-642-24541-1_27 https://math.stackexchange.com/questions/2090523/ https://math.stackexchange.com/questions/35671/ https://web.archive.org/web/20161024183030/http:/www.maths.lth.se/matematiklu/personal/jaak/hypergf.ps https://www.jstor.org/stable/2003310 https://www.jstor.org/stable/2309789 http://doi.org/10.1007/BF03029866 http://doi.org/10.1017/s0305004100016558%C2%A0 http://doi.org/10.1515/crll.1869.70.105 https://case.edu/artsci/math/langer/jlpreprints/Trefoil.pdf https://www.desmos.com/calculator/5s4gdcnxh2. https://www.desmos.com/calculator/elqqf4nwas https://archive.org/details/conformalproject0000leel
sameAs	Dixon elliptic functions Dixon elliptic functions
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has abstract	In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane. Because these functions satisfy the identity , as real functions they parametrize the cubic Fermat curve , just as the trigonometric functions sine and cosine parametrize the unit circle . They were named sm and cm by Alfred Dixon in 1890, by analogy to the trigonometric functions sine and cosine and the Jacobi elliptic functions sn and cn; Göran Dillner described them earlier in 1873. (en)
prov:wasDerivedFrom	wikipedia-en:Dixon_elliptic_functions?oldid=1121913630&ns=0
page length (characters) of wiki page	20613 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Dixon_elliptic_functions
is Link from a Wikipage to another Wikipage of	Doubly periodic function Jacobi elliptic functions Eisenstein integer

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