In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied...

related to the lemniscate elliptic functions and approximately equal to 2.62205755. It also appears in evaluation of the gamma and beta function at certain...

elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. There are twelve Jacobi elliptic functions...

upper half space. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables...

Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also...

analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because...

In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map...

of arcs of the lemniscate leads to elliptic integrals, as was discovered in the eighteenth century. Around 1800, the elliptic functions inverting those...

other. The lemniscatic elliptic functions are analogues of trigonometric functions for the lemniscate of Bernoulli, and the lemniscate constants arise in...

Weierstrass's elliptic functions Lemniscate elliptic functions Theta functions Neville theta functions Modular lambda function Closely related are the...

elliptic functions Euler's formula Generalized trigonometry Hyperbolic function Lemniscate elliptic functions Law of sines List of periodic functions...

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

functions. In particular, the arc lengths of ellipses and of the lemniscate, which are curves defined by algebraic equations, are given by elliptic integrals...

Stockton-Lindquist House, DeLand, Florida, US Lemniscate elliptic functions § Hyperbolic lemniscate functions Vanua Lava Airport, Vanuatu, IATA code SLH-DSA...

generate chaotic dynamical systems on a square, and the lemniscate elliptic functions, complex functions periodic on a square grid. A square is inscribed in...

division of arcs of certain curves, especially the lemniscate (cf. Lemniscate elliptic functions); this seems also to have been in his own estimation...

}(-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}]} be a...

{\displaystyle \Gamma \left({\tfrac {1}{4}}\right)} is related to the lemniscate constant ϖ {\displaystyle \varpi } by Γ ( 1 4 ) = 2 ϖ 2 π {\displaystyle...

specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function is of great importance...

used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some mathematical constants, in particular,...

Hyperbolic lemniscate cotangent. For the derivation of this, please see the Wikipedia article lemniscate elliptic functions! The elliptic nome of this...

is known, at least when A is an elliptic curve. The question of the rank is thought to be bound up with L-functions (see below). The torsor theory here...

– trigonometric identities for multiple distinct angles The Lemniscate elliptic functions, sinlem and coslem The Pythagorean theorem in non-Euclidean...

exponential function in a Gauss sum is replaced by an elliptic function. They were introduced by Eisenstein (1850), at least in the lemniscate case when...

{2}}\operatorname {sl} \left(w\right)} is the lemniscatic sine function (see Lemniscate elliptic functions). According to Peirce, his projection has the following...

volume Chlorine, symbol Cl, a chemical element cl (elliptic function), cosine lemniscate function Clifford algebra, denoted Cl Confidence level Divisor...

curve Hippopede Kampyle of Eudoxus Kappa curve Lemniscate Lemniscate of Booth Lemniscate of Gerono Lemniscate of Bernoulli Limaçon Cardioid Limaçon trisectrix...

section Elliptic curve Fractional ideal Function field of an algebraic variety Function field (scheme theory) Genus (mathematics) Polynomial lemniscate Quartic...

of straightedge-and-compass elliptic division appears to be unknown, unlike in the case of the circle and the lemniscate. The division in special cases...

(complexity), a class of computational complexity sl (elliptic function), sine lemniscate function Special linear group in mathematics, denoted SLn or SL(n)...