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- Lemniscatic_elliptic_function abstract "In mathematics, a lemniscatic elliptic function is an elliptic function related to the arc length of a lemniscate of Bernoulli studied by Giulio Carlo de' Toschi di Fagnano in 1718. It has a square period lattice and is closely related to the Weierstrass elliptic function when the Weierstrass invariants satisfy g2 = 1 and g3 = 0. In the lemniscatic case, the minimal half period ω1 is real and equal to where Γ is the Gamma function. The second smallest half period is pure imaginary and equal to iω1. In more algebraic terms, the period lattice is a real multiple of the Gaussian integers.The constants e1, e2, and e3 are given byThe case g2 = a, g3 = 0 may be handled by a scaling transformation. However, this may involve complex numbers. If it is desired to remain within real numbers, there are two cases to consider: a > 0 and a < 0. The period paralleogram is either a "square" or a "diamond".".
- Lemniscatic_elliptic_function thumbnail Lemniscate_of_Bernoulli.svg?width=300.
- Lemniscatic_elliptic_function wikiPageID "3754835".
- Lemniscatic_elliptic_function wikiPageRevisionID "587154772".
- Lemniscatic_elliptic_function first "P.L.".
- Lemniscatic_elliptic_function first "W.P.".
- Lemniscatic_elliptic_function hasPhotoCollection Lemniscatic_elliptic_function.
- Lemniscatic_elliptic_function id "23.5".
- Lemniscatic_elliptic_function id "p/l058120".
- Lemniscatic_elliptic_function last "Reinhardt".
- Lemniscatic_elliptic_function last "Walker".
- Lemniscatic_elliptic_function title "Lemniscate functions".
- Lemniscatic_elliptic_function title "Lemniscate lattice".
- Lemniscatic_elliptic_function subject Category:Elliptic_curves.
- Lemniscatic_elliptic_function subject Category:Elliptic_functions.
- Lemniscatic_elliptic_function subject Category:Modular_forms.
- Lemniscatic_elliptic_function type Abstraction100002137.
- Lemniscatic_elliptic_function type Attribute100024264.
- Lemniscatic_elliptic_function type Curve113867641.
- Lemniscatic_elliptic_function type EllipticCurves.
- Lemniscatic_elliptic_function type EllipticFunctions.
- Lemniscatic_elliptic_function type Form106290637.
- Lemniscatic_elliptic_function type Function113783816.
- Lemniscatic_elliptic_function type LanguageUnit106284225.
- Lemniscatic_elliptic_function type Line113863771.
- Lemniscatic_elliptic_function type MathematicalRelation113783581.
- Lemniscatic_elliptic_function type ModularForms.
- Lemniscatic_elliptic_function type Part113809207.
- Lemniscatic_elliptic_function type Relation100031921.
- Lemniscatic_elliptic_function type Shape100027807.
- Lemniscatic_elliptic_function type Word106286395.
- Lemniscatic_elliptic_function comment "In mathematics, a lemniscatic elliptic function is an elliptic function related to the arc length of a lemniscate of Bernoulli studied by Giulio Carlo de' Toschi di Fagnano in 1718. It has a square period lattice and is closely related to the Weierstrass elliptic function when the Weierstrass invariants satisfy g2 = 1 and g3 = 0. In the lemniscatic case, the minimal half period ω1 is real and equal to where Γ is the Gamma function.".
- Lemniscatic_elliptic_function label "Funkcje lemniskaty".
- Lemniscatic_elliptic_function label "Lemniscatic elliptic function".
- Lemniscatic_elliptic_function sameAs Funkcje_lemniskaty.
- Lemniscatic_elliptic_function sameAs m.09z6x2.
- Lemniscatic_elliptic_function sameAs Q6521248.
- Lemniscatic_elliptic_function sameAs Q6521248.
- Lemniscatic_elliptic_function sameAs Lemniscatic_elliptic_function.
- Lemniscatic_elliptic_function wasDerivedFrom Lemniscatic_elliptic_function?oldid=587154772.
- Lemniscatic_elliptic_function depiction Lemniscate_of_Bernoulli.svg.
- Lemniscatic_elliptic_function isPrimaryTopicOf Lemniscatic_elliptic_function.
