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- ...on elliptic functions cm, sm applied to a real-valued argument ''x''. Both functions are periodic with real period {{math|''π''<sub>3</sub> ≈ 5.29991625}}]] ...+ \operatorname{sm}^3 z = 1</math>, as [[function of a real variable|real functions]] they parametrize the cubic [[Fermat curve]] <math>x^3 + y^3 = 1</math>, j ...28 KB (3,851 words) - 05:23, 28 December 2024
- ...theoriae functionum ellipticarum]]'' became the standard work on elliptic functions.<ref name=:84f>{{citation|last=Gray|first=Jeremy|title=Real and the complex ...continued to explore these functions. He also tried to generalize them to functions with even more periods, but seemed to be in no hurry to publish his results ...10 KB (1,671 words) - 21:24, 31 December 2024
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- {{short description|Theorem on a polynomial involving the elliptic modular function}} for ''j'' the [[elliptic modular function]] and τ running through classes of imaginary quadratic int ...924 bytes (126 words) - 02:54, 21 June 2020
- ...tric functions]] and [[elliptic functions]]. This article describes these functions and the corresponding solutions for the orbits. ...handful of forces result in formulae for <math>u</math> in terms of known functions. The solution for <math>\varphi</math> can be expressed as an integral ove ...2 KB (344 words) - 08:07, 28 January 2021
- ...ic integral of the second kind]] and sn, cn and dn are [[Jacobi's elliptic functions]].<ref name="oprea" /> ...1,019 bytes (163 words) - 21:26, 29 December 2024
- ...ated results in the [[mathematical]] study of the regularity of [[harmonic functions]] on sufficiently smooth domains by [[Oliver Dimon Kellogg]]. ...of the boundary are [[Dini continuity|Dini continuous]], then the harmonic functions are uniformly <math>C^k</math> as well. The second, more common version of ...2 KB (252 words) - 10:50, 23 October 2022
- {{for|other θ functions|Theta function (disambiguation)}} ...unctions.wolfram.com/EllipticFunctions/NevilleThetaC/02/ The Mathematical Functions Site]</ref> ...4 KB (588 words) - 05:34, 10 May 2024
- ...coordinates of the varying point on this curve are given by the [[Jacobian elliptic function]]s. ...ion]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Jacobi Elliptic Functions |url=https://mathworld.wolfram.com/ |access-date=2023-01-31 |website=mathwo ...3 KB (473 words) - 17:42, 26 July 2024
- {{Short description|Mathematical method in elliptic functions}} ...ptic integral]], useful for the efficient numerical evaluation of elliptic functions. It was originally due to [[John Landen]] and independently rediscovered by ...6 KB (905 words) - 23:31, 5 October 2024
- ...th>L^{\lambda,p}(\Omega)</math> are [[Hölder condition|Hölder continuous]] functions over the domain <math>\Omega</math>. ...}</math>. For <math>\lambda > n+p</math>, the space contains only constant functions. ...3 KB (468 words) - 13:34, 19 January 2020
- ...on]] that projects the globe onto a [[tetrahedron]] using [[Dixon elliptic functions]]. It is conformal everywhere except for the four singularities at the vert | title = Some Conformal Projections Based on Elliptic Functions ...3 KB (393 words) - 23:48, 27 December 2024
- ...in terms of complete elliptic integrals. It was introduced (for complete elliptic integrals) by {{harvs|txt|first=A. M. |last=Legendre|authorlink=A. M. Legen ==Complete elliptic integrals== ...10 KB (1,485 words) - 21:50, 2 March 2023
- {{Short description|Elliptic analog of hypergeometric series}} In mathematics, an '''elliptic hypergeometric series''' is a series Σ''c''<sub>''n''</sub> such that the r ...6 KB (928 words) - 04:58, 22 January 2024
- {{Short description|Prime number with a certain relationship to an elliptic curve}} ...od reduction#G|reduction]] of ''E'' modulo ''p'' is a [[supersingular elliptic curve]] over the [[residue field]] '''F'''<sub>''p''</sub>. ...3 KB (432 words) - 11:11, 15 September 2024
- ...a ''fundamental period''. A definition is given for some of the following functions, though each function may have many equivalent definitions. == Smooth functions == ...9 KB (1,415 words) - 03:24, 21 January 2025
- {{Short description|Gauss sum on an elliptic curve}} ...ue symbol, and the exponential function in a Gauss sum is replaced by an [[elliptic function]]. ...4 KB (568 words) - 21:52, 21 December 2023
- ...sion points. They play a central role in the study of [[counting points on elliptic curves]] in [[Schoof's algorithm]]. * The division polynomials form a generic [[elliptic divisibility sequence]] over the ring <math>\mathbb{Q}[x,y,A,B]/(y^2-x^3-Ax ...5 KB (844 words) - 14:19, 28 December 2023
- ...ons]]. It is another name for the stronger version of [[Montel%27s theorem#Functions omitting two values|Montel's theorem]]. Let <math>\mathcal{F} </math> be a family of analytic functions defined on a domain <math> \Omega </math>. If there are two fixed complex n ...1,003 bytes (147 words) - 15:51, 1 August 2022
- ...theoriae functionum ellipticarum]]'' became the standard work on elliptic functions.<ref name=:84f>{{citation|last=Gray|first=Jeremy|title=Real and the complex ...continued to explore these functions. He also tried to generalize them to functions with even more periods, but seemed to be in no hurry to publish his results ...10 KB (1,671 words) - 21:24, 31 December 2024
- ...dor|first3=Tiago|date=2016-05-14|title=Numerical methods for the 2-Hessian elliptic partial differential equation|url=http://dx.doi.org/10.1093/imanum/drw007|j ...the ''2−''hessian equation is unfamiliar outside Riemannian geometry and elliptic regularity theory, that is closely related to the scalar curvature operator ...4 KB (548 words) - 17:55, 23 December 2023
- ...or the '''''p''-Laplace operator''', is a quasilinear [[elliptic operator|elliptic]] [[partial differential operator]] of 2nd order. It is a nonlinear general ...th>\Omega</math> has a smooth boundary, this is equivalent to require that functions coincide with the boundary datum in [[Trace operator|trace]] sense<ref name ...5 KB (641 words) - 16:31, 27 December 2024
- ...[Hilbert's nineteenth problem]] was concerned with this concept.<ref name="Elliptic"/> == Elliptic regularity theory == ...5 KB (852 words) - 11:50, 21 February 2025