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- Elliptic_function abstract "In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles (counting multiplicity) in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying that the residues of any simple poles must cancel. Historically, elliptic functions were first discovered by Niels Henrik Abel as inverse functions of elliptic integrals, and their theory improved by Carl Gustav Jacobi; these in turn were studied in connection with the problem of the arc length of an ellipse, whence the name derives. Jacobi's elliptic functions have found numerous applications in physics, and were used by Jacobi to prove some results in elementary number theory. A more complete study of elliptic functions was later undertaken by Karl Weierstrass, who found a simple elliptic function in terms of which all the others could be expressed. Besides their practical use in the evaluation of integrals and the explicit solution of certain differential equations, they have deep connections with elliptic curves and modular forms.".
- Elliptic_function wikiPageExternalLink 1.
- Elliptic_function wikiPageExternalLink ?pa=content&sa=viewDocument&nodeId=1557.
- Elliptic_function wikiPageID "69939".
- Elliptic_function wikiPageRevisionID "584313206".
- Elliptic_function hasPhotoCollection Elliptic_function.
- Elliptic_function id "p/e035470".
- Elliptic_function title "Elliptic function".
- Elliptic_function subject Category:Elliptic_functions.
- Elliptic_function type Abstraction100002137.
- Elliptic_function type EllipticFunctions.
- Elliptic_function type Function113783816.
- Elliptic_function type MathematicalRelation113783581.
- Elliptic_function type Relation100031921.
- Elliptic_function comment "In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant.".
- Elliptic_function label "Elliptic function".
- Elliptic_function label "Elliptische Funktion".
- Elliptic_function label "Elliptische functie".
- Elliptic_function label "Fonction elliptique".
- Elliptic_function label "Función elíptica".
- Elliptic_function label "Funkcje eliptyczne".
- Elliptic_function label "Funzioni ellittiche".
- Elliptic_function label "Função elíptica".
- Elliptic_function label "Эллиптическая функция".
- Elliptic_function label "دالة إهليلجية".
- Elliptic_function label "楕円函数".
- Elliptic_function label "橢圓函數".
- Elliptic_function sameAs Elliptische_Funktion.
- Elliptic_function sameAs Función_elíptica.
- Elliptic_function sameAs Fonction_elliptique.
- Elliptic_function sameAs Funzioni_ellittiche.
- Elliptic_function sameAs 楕円函数.
- Elliptic_function sameAs 타원함수.
- Elliptic_function sameAs Elliptische_functie.
- Elliptic_function sameAs Funkcje_eliptyczne.
- Elliptic_function sameAs Função_elíptica.
- Elliptic_function sameAs m.0j5s3.
- Elliptic_function sameAs Q938102.
- Elliptic_function sameAs Q938102.
- Elliptic_function sameAs Elliptic_function.
- Elliptic_function wasDerivedFrom Elliptic_function?oldid=584313206.
- Elliptic_function isPrimaryTopicOf Elliptic_function.