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...It has a square period lattice and is closely related to the [[Weierstrass elliptic function]] when the Weierstrass invariants satisfy {{math|''g''<sub>2</sub They are doubly periodic (or elliptic) functions in the complex plane, with periods {{math|2{{pi}}''G''}} and {{m ...

...] and [[Leonhard Euler]] ({{Circa|1750}}). Modern mathematics defines an "elliptic integral" as any [[function (mathematics)|function]] {{math|''f''}} which c ...nctions and the three [[Legendre form|Legendre canonical form]]s (i.e. the elliptic integrals of the first, second and third kind). ...

...ng its behavior with respect to the addition of a period of the associated elliptic functions, making it a [[quasiperiodic function]]. In the abstract theory t ...used to define a variety of [[modular forms]], and to parametrize certain curves; in particular, the '''Jacobi identity''' is ...

...pse.<ref name="Lawrence">Lawrence, J. Dennis, ''A Catalog of Special Plane Curves'', Dover Publ., 1972.</ref>{{rp|p.63}} ...only used in [[Computer Aided Design]] (see [[Bezier curve#Rational Bézier curves|Bezier curve]]). ...

...[[partial differential equation]] [[boundary value problem]]s possessing [[elliptic]]{{Disambiguation needed|date=August 2020}} symmetry.<ref name="Gutiérrez-V ...ely. They are sometimes also referred to as ''cosine-elliptic'' and ''sine-elliptic'', or '''Mathieu functions of the first kind'''. ...

...ny continuous extensions of the factorial to non-integers: infinitely many curves can be drawn through any set of isolated points. The gamma function is the ...niscate]], which are curves defined by algebraic equations, are given by [[elliptic integral]]s that in special cases can be evaluated in terms of the gamma fu ...