Elliptic function information

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

In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see...

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

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

In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined...

sections of a line bundle on the moduli stack of elliptic curves. A modular function is a function that is invariant with respect to the modular group...

filter becomes a Butterworth filter. The gain of a lowpass elliptic filter as a function of angular frequency ω is given by: G n ( ω ) = 1 1 + ϵ 2 R...

In mathematics Abel elliptic functions are a special kind of elliptic functions, that were established by the Norwegian mathematician Niels Henrik Abel...

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

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

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

cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography...

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

Weierstrass sigma function, related to elliptic functions Rado's sigma function, see busy beaver See also sigmoid function. This disambiguation page lists mathematics...

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

In mathematics, an elliptic hypergeometric series is a series Σcn such that the ratio cn/cn−1 is an elliptic function of n, analogous to generalized hypergeometric...

mathematics, the elliptic gamma function is a generalization of the q-gamma function, which is itself the q-analog of the ordinary gamma function. It is closely...

type DirectShow, Microsoft API Nintendo DS ds (elliptic function), one of Jacobi's elliptic functions De Sitter space (dS) Down syndrome, a genetic disorder...

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...

mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used...

was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory...

smooth functions (if the coefficients in the operator are smooth). Steady-state solutions to hyperbolic and parabolic equations generally solve elliptic equations...

)^{4}}}x^{2n}\end{aligned}}} The Jacobi theta functions describe the world of the elliptic modular functions and they have these Taylor series: ϑ 00 ( x...

square of the elliptic modulus, that is, λ ( τ ) = k 2 ( τ ) {\displaystyle \lambda (\tau )=k^{2}(\tau )} . In terms of the Dedekind eta function η ( τ ) {\displaystyle...