mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class...

mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named...

equation is called a Weierstrass equation, and said to be in Weierstrass form, or Weierstrass normal form. The definition of elliptic curve also requires...

{\displaystyle \sin } . The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions...

Eisenstein integer Elliptic function Abel elliptic functions Jacobi elliptic functions Lemniscate elliptic functions Weierstrass elliptic function Lee conformal...

of an ellipse. Important elliptic functions are Jacobi elliptic functions and the Weierstrass ℘ {\displaystyle \wp } -function. Further development of...

quotients of the above four theta functions, and could have been used by him to construct Weierstrass's elliptic functions also, since ℘ ( z ; τ ) = − ( log...

Bolzano–Weierstrass theorem Stone–Weierstrass theorem Casorati–Weierstrass theorem Weierstrass elliptic function Weierstrass function Weierstrass M-test...

modeling. Elliptic function Abel elliptic functions Dixon elliptic functions Jacobi elliptic functions Weierstrass elliptic function Elliptic Gauss sum...

and in particular the study of Weierstrass elliptic functions, the equianharmonic case occurs when the Weierstrass invariants satisfy g2 = 0 and g3 = 1...

Elliptic functions: The inverses of elliptic integrals; used to model double-periodic phenomena. Jacobi's elliptic functions Weierstrass's elliptic functions...

Elliptic curve Schwarz–Christoffel mapping Carlson symmetric form Jacobi's elliptic functions Weierstrass's elliptic functions Jacobi theta function Ramanujan...

modular forms. In particular the modular discriminant of the Weierstrass elliptic function with ω 2 = τ ω 1 {\displaystyle \omega _{2}=\tau \omega _{1}}...

theorem Weierstrass coordinates Weierstrass's elliptic functions Weierstrass equation Weierstrass factorization theorem Weierstrass function Weierstrass functions...

the elliptic curve y 2 = 4 x 3 − g 2 ( τ ) x − g 3 ( τ ) {\displaystyle y^{2}=4x^{3}-g_{2}(\tau )x-g_{3}(\tau )} (see Weierstrass elliptic functions). Note...

‣ Modular Functions ‣ Chapter 23 Weierstrass Elliptic and Modular Functions". dlmf.nist.gov. Retrieved 2023-07-07. A meromorphic function can only have...

by sigma function one can mean one of the following: The sum-of-divisors function σa(n), an arithmetic function Weierstrass sigma function, related to...

Y\to \pm iY,\quad X\to -X} in line with the action of i on the Weierstrass elliptic functions. More generally, consider the lattice Λ, an additive group in...

Spirograph (special case of the hypotrochoid) Jacobi's elliptic functions Weierstrass's elliptic function Formulae are given as Taylor series or derived from...

function with just one zero. Elliptic function Abel elliptic functions Jacobi elliptic functions Weierstrass elliptic functions Lemniscate elliptic functions...

in the Armenian alphabet Weierstrass p (also called "pe"), a mathematical letter (℘) used in Weierstrass's elliptic functions and power sets Péclet number...

elliptic integrals and the Jacobi or Weierstrass elliptic functions. Jacobi was the first to apply elliptic functions to number theory, for example proving...

function in Weierstrass's elliptic functions Delta function potential, in quantum mechanics, a potential well described by the Dirac delta function Delta-functor...

and the Costa's minimal surface. Costa's surface involves Weierstrass's elliptic function ℘ {\displaystyle \wp } : g ( ω ) = A ℘ ′ ( ω ) {\displaystyle...

ratio Jacobi's elliptic functions Weierstrass's elliptic functions Theta function Elliptic modular function J-function Modular function Modular form Analytic...

(Z + τZ) is sent to (x, y) = (℘(z), ℘′(z)), where ℘ is the Weierstrass elliptic function. Likewise, genus g surfaces have Riemann surface structures...

}(-1)^{n}e^{\pi i\tau n^{2}}} In terms of the half-periods of Weierstrass's elliptic functions, let [ ω 1 , ω 2 ] {\displaystyle [\omega _{1},\omega _{2}]}...

fact about elliptic operators, of which the Laplacian is a major example. The uniform limit of a convergent sequence of harmonic functions is still harmonic...

The Costa surface can be described using the Weierstrass zeta and the Weierstrass elliptic functions. Costa, Celso José da (1982). Imersões mínimas...

ω2 are the periods of the Weierstrass elliptic function, and η1 and η2 are the quasiperiods of the Weierstrass zeta function. Some authors normalize these...