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- Elliptic_integral abstract "In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler. Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form where R is a rational function of its two arguments, P is a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.In general, integrals in this form cannot be expressed in terms of elementary functions. Exceptions to this general rule are when P has repeated roots, or when R(x,y) contains no odd powers of y. However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms (i.e. the elliptic integrals of the first, second and third kind).Besides the Legendre form given below, the elliptic integrals may also be expressed in Carlson symmetric form. Additional insight into the theory of the elliptic integral may be gained through the study of the Schwarz–Christoffel mapping. Historically, elliptic functions were discovered as inverse functions of elliptic integrals.".
- Elliptic_integral wikiPageExternalLink pg=613.
- Elliptic_integral wikiPageExternalLink pg=309.
- Elliptic_integral wikiPageExternalLink elliptic.googlecode.com.
- Elliptic_integral wikiPageExternalLink EllipticIntegral.html.
- Elliptic_integral wikiPageExternalLink rtx120801094p.pdf.
- Elliptic_integral wikiPageExternalLink applicationselli00greerich.
- Elliptic_integral wikiPageExternalLink lecturestheorell00hancrich.
- Elliptic_integral wikiPageExternalLink onthenumerical032686mbp.
- Elliptic_integral wikiPageExternalLink ellipint.html.
- Elliptic_integral wikiPageExternalLink gr.
- Elliptic_integral wikiPageID "9960".
- Elliptic_integral wikiPageRevisionID "593229485".
- Elliptic_integral first "B.C.".
- Elliptic_integral hasPhotoCollection Elliptic_integral.
- Elliptic_integral id "19".
- Elliptic_integral id "p/e035490".
- Elliptic_integral last "Carlson".
- Elliptic_integral title "Elliptic integral".
- Elliptic_integral subject Category:Elliptic_functions.
- Elliptic_integral subject Category:Special_hypergeometric_functions.
- Elliptic_integral type Abstraction100002137.
- Elliptic_integral type EllipticFunctions.
- Elliptic_integral type Function113783816.
- Elliptic_integral type MathematicalRelation113783581.
- Elliptic_integral type Relation100031921.
- Elliptic_integral type SpecialHypergeometricFunctions.
- Elliptic_integral comment "In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler.".
- Elliptic_integral label "Całki eliptyczne".
- Elliptic_integral label "Elliptic integral".
- Elliptic_integral label "Elliptische integraal".
- Elliptic_integral label "Elliptisches Integral".
- Elliptic_integral label "Integral elíptica".
- Elliptic_integral label "Integral elíptica".
- Elliptic_integral label "Integrale ellittico".
- Elliptic_integral label "Intégrale elliptique".
- Elliptic_integral label "Эллиптический интеграл".
- Elliptic_integral label "椭圆积分".
- Elliptic_integral label "楕円積分".
- Elliptic_integral sameAs Elliptisches_Integral.
- Elliptic_integral sameAs Integral_elíptica.
- Elliptic_integral sameAs Intégrale_elliptique.
- Elliptic_integral sameAs Integrale_ellittico.
- Elliptic_integral sameAs 楕円積分.
- Elliptic_integral sameAs Elliptische_integraal.
- Elliptic_integral sameAs Całki_eliptyczne.
- Elliptic_integral sameAs Integral_elíptica.
- Elliptic_integral sameAs m.02q5n.
- Elliptic_integral sameAs Q1126603.
- Elliptic_integral sameAs Q1126603.
- Elliptic_integral sameAs Elliptic_integral.
- Elliptic_integral wasDerivedFrom Elliptic_integral?oldid=593229485.
- Elliptic_integral isPrimaryTopicOf Elliptic_integral.