Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Elliptic_function> ?p ?o }
- 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 was 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.".
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- Elliptic_function wikiPageRevisionID "679902573".
- Elliptic_function wikiPageWikiLink A_Course_of_Modern_Analysis.
- Elliptic_function wikiPageWikiLink Arc_length.
- Elliptic_function wikiPageWikiLink Bounded_function.
- Elliptic_function wikiPageWikiLink Carl_Gustav_Jacob_Jacobi.
- Elliptic_function wikiPageWikiLink Carl_Gustav_Jacobi.
- Elliptic_function wikiPageWikiLink Category:Elliptic_functions.
- Elliptic_function wikiPageWikiLink Complex_analysis.
- Elliptic_function wikiPageWikiLink Complex_plane.
- Elliptic_function wikiPageWikiLink Contour_integral.
- Elliptic_function wikiPageWikiLink Derivative.
- Elliptic_function wikiPageWikiLink Doubly_periodic_function.
- Elliptic_function wikiPageWikiLink E._T._Whittaker.
- Elliptic_function wikiPageWikiLink Ellipse.
- Elliptic_function wikiPageWikiLink Elliptic_curve.
- Elliptic_function wikiPageWikiLink Elliptic_integral.
- Elliptic_function wikiPageWikiLink Entire_function.
- Elliptic_function wikiPageWikiLink Field_(mathematics).
- Elliptic_function wikiPageWikiLink Function_(mathematics).
- Elliptic_function wikiPageWikiLink Fundamental_parallelogram.
- Elliptic_function wikiPageWikiLink G._N._Watson.
- Elliptic_function wikiPageWikiLink Holomorphic_function.
- Elliptic_function wikiPageWikiLink Inverse_function.
- Elliptic_function wikiPageWikiLink J-invariant.
- Elliptic_function wikiPageWikiLink Jacobi_elliptic_functions.
- Elliptic_function wikiPageWikiLink Jacobis_elliptic_functions.
- Elliptic_function wikiPageWikiLink Karl_Weierstrass.
- Elliptic_function wikiPageWikiLink Laurent_series.
- Elliptic_function wikiPageWikiLink Linear_fractional_transformation.
- Elliptic_function wikiPageWikiLink Liouvilles_theorem_(complex_analysis).
- Elliptic_function wikiPageWikiLink Meromorphic.
- Elliptic_function wikiPageWikiLink Meromorphic_function.
- Elliptic_function wikiPageWikiLink Methods_of_contour_integration.
- Elliptic_function wikiPageWikiLink Modular_form.
- Elliptic_function wikiPageWikiLink Modular_function.
- Elliptic_function wikiPageWikiLink Modular_group.
- Elliptic_function wikiPageWikiLink Naum_Akhiezer.
- Elliptic_function wikiPageWikiLink Niels_Henrik_Abel.
- Elliptic_function wikiPageWikiLink Normal_convergence.
- Elliptic_function wikiPageWikiLink Periodic_function.
- Elliptic_function wikiPageWikiLink Pole_(complex_analysis).
- Elliptic_function wikiPageWikiLink Quarter_period.
- Elliptic_function wikiPageWikiLink Ramanujan_theta_function.
- Elliptic_function wikiPageWikiLink Residue_theorem.
- Elliptic_function wikiPageWikiLink Tom_M._Apostol.
- Elliptic_function wikiPageWikiLink Weierstrasss_elliptic_functions.
- Elliptic_function wikiPageWikiLink Whittaker_and_Watson.
- Elliptic_function wikiPageWikiLink File:JacobiFunctionAbstract.png.
- Elliptic_function wikiPageWikiLinkText "Elliptic Functions".
- Elliptic_function wikiPageWikiLinkText "Elliptic function".
- Elliptic_function wikiPageWikiLinkText "elliptic function field".
- Elliptic_function wikiPageWikiLinkText "elliptic function".
- Elliptic_function wikiPageWikiLinkText "elliptic".
- Elliptic_function hasPhotoCollection Elliptic_function.
- Elliptic_function id "p/e035470".
- Elliptic_function title "Elliptic function".
- Elliptic_function wikiPageUsesTemplate Template:Abramowitz_Stegun_ref2.
- Elliptic_function wikiPageUsesTemplate Template:Commons_category.
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- Elliptic_function wikiPageUsesTemplate Template:Refend.
- Elliptic_function wikiPageUsesTemplate Template:Reflist.
- Elliptic_function wikiPageUsesTemplate Template:Springer.
- Elliptic_function subject Category:Elliptic_functions.
- Elliptic_function hypernym Function.
- Elliptic_function type ProgrammingLanguage.
- Elliptic_function type Type.
- Elliptic_function type Function.
- Elliptic_function type Type.
- 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 sameAs دالة_إهليلجية.
- Elliptic_function sameAs Funció_el·líptica.
- Elliptic_function sameAs Elliptische_Funktion.
- Elliptic_function sameAs Función_elíptica.
- Elliptic_function sameAs تابع_بیضوی.
- Elliptic_function sameAs Elliptinen_funktio.
- Elliptic_function sameAs Fonction_elliptique.
- Elliptic_function sameAs פונקציה_אליפטית.
- Elliptic_function sameAs Funzione_ellittica.
- Elliptic_function sameAs 楕円函数.
- Elliptic_function sameAs Эллиптік_функция.
- Elliptic_function sameAs 타원함수.
- Elliptic_function sameAs Elliptische_functie.
- Elliptic_function sameAs Elliptisk_funksjon.
- Elliptic_function sameAs Elliptiske_funksjoner.
- Elliptic_function sameAs Funkcje_eliptyczne.
- Elliptic_function sameAs Função_elíptica.
- Elliptic_function sameAs m.0j5s3.
- Elliptic_function sameAs Funcție_eliptică.
- Elliptic_function sameAs Эллиптическая_функция.
- Elliptic_function sameAs Elliptisk_funktion.
- Elliptic_function sameAs Еліптична_функція.
- Elliptic_function sameAs Q938102.