AI & ChatGPT searches , social queries for ELLIPTIC FUNCTION
Search references for ELLIPTIC FUNCTION. Phrases containing ELLIPTIC FUNCTION
See searches and references containing ELLIPTIC FUNCTION!
Search references for ELLIPTIC FUNCTION. Phrases containing ELLIPTIC FUNCTION
See searches and references containing ELLIPTIC FUNCTION!ELLIPTIC FUNCTION
Class of periodic mathematical functions
analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because
Elliptic_function
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Class of mathematical functions
Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also
Weierstrass_elliptic_function
Mathematical function
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, as
Jacobi_elliptic_functions
Special function defined by an integral
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
Elliptic_integral
In mathematics Abel elliptic functions are a special kind of elliptic functions, that were established by the Norwegian mathematician Niels Henrik Abel
Abel_elliptic_functions
Algebraic curve in mathematics
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
Elliptic_curve
In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map
Dixon_elliptic_functions
Signal processing filter
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
Elliptic_filter
Analytic function on the upper half-plane with a certain behavior under the modular group
j(z) of an elliptic curve, regarded as a function on the set of all elliptic curves, is a modular function. More conceptually, modular functions can be thought
Modular_form
Elliptic functions: The inverses of elliptic integrals; used to model double-periodic phenomena. Jacobi's elliptic functions Weierstrass's elliptic functions
List of mathematical functions
List_of_mathematical_functions
Mathematic function
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
Elliptic_gamma_function
Symmetric holomorphic function
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
Modular_lambda_function
Mathematical functions related to Weierstrass's elliptic function
mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for
Weierstrass_functions
Special functions of several complex variables
properties of elliptic curves?" and others, including abelian varieties, moduli spaces, quadratic forms, and solitons. Theta functions in two dimensions
Theta_function
Spirograph (special case of the hypotrochoid) Jacobi's elliptic functions Weierstrass's elliptic function Formulae are given as Taylor series or derived from
List_of_periodic_functions
Mathematical function
forms. In particular the modular discriminant of the Weierstrass elliptic function with ω 2 = τ ω 1 {\displaystyle \omega _{2}=\tau \omega _{1}} can
Dedekind_eta_function
Elliptic analog of hypergeometric series
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
Elliptic hypergeometric series
Elliptic_hypergeometric_series
Modular function in mathematics
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
J-invariant
Topics referred to by the same term
Weierstrass sigma function, related to elliptic functions Rado's sigma function, see busy beaver See also sigmoid function. This disambiguation page lists mathematics
Sigma_function
Solutions of Lamé's equation
the elliptic sine function, and κ 2 = n ( n + 1 ) k 2 {\displaystyle \kappa ^{2}=n(n+1)k^{2}} for an integer n and k {\displaystyle k} the elliptic modulus
Lamé_function
mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used
Elliptic_rational_functions
Function with two complex number "periods"
function with just one zero. Elliptic function Abel elliptic functions Jacobi elliptic functions Weierstrass elliptic functions Lemniscate elliptic functions
Doubly_periodic_function
German mathematician (1804–1851)
was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants and number theory
Carl_Gustav_Jacob_Jacobi
Algebraic curve
function is an element of the function field of such a curve, or of the Jacobian variety on the curve; these two concepts are identical for elliptic functions
Hyperelliptic_curve
Special mathematical function
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
Nome_(mathematics)
Theory of a class of elliptic curves
theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with extra
Complex_multiplication
Elliptic functions
In mathematics, the half-period ratio τ of an elliptic function is the ratio τ = ω 2 ω 1 {\displaystyle \tau ={\frac {\omega _{2}}{\omega _{1}}}} of the
Half-period_ratio
Key agreement protocol
Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish
Elliptic-curve_Diffie–Hellman
Free swinging suspended body
solution. The Jacobian elliptic function that expresses the position of a pendulum as a function of time is a doubly periodic function with a real period
Pendulum_(mechanics)
Topics referred to by the same term
Core, a metadata standard Dynamic contrast, an LCD technology dc (elliptic function), in complex analysis Axiom of dependent choice, in set theory DC
DC
Mathematical function
particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In
Ramanujan_theta_function
Mathematical function associated to algebraic varieties
global L-function; this would be a vast generalisation of the Taniyama-Weil conjecture, itself an important result in number theory. For an elliptic curve
Hasse–Weil_zeta_function
Plane algebraic curve
the lemniscate leads to elliptic integrals, as was discovered in the eighteenth century. Around 1800, the elliptic functions inverting those integrals
Lemniscate_of_Bernoulli
Cryptographic algorithm for digital signatures
cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography
Elliptic Curve Digital Signature Algorithm
Elliptic_Curve_Digital_Signature_Algorithm
Mathieu equations, in his “Memoir on vibrations of an elliptic membrane” in 1868. "Mathieu functions are applicable to a wide variety of physical phenomena
Mathieu_wavelet
One-dimensional complex manifold
(z),\wp '(z))} , where ℘ {\displaystyle \wp } is the Weierstrass elliptic function. Likewise, genus g {\displaystyle g} surfaces have Riemann surface
Riemann_surface
Term used in the theories of Riemann surfaces and algebraic curves
Weierstrass zeta function was called an integral of the second kind in elliptic function theory; it is a logarithmic derivative of a theta function, and therefore
Differential of the first kind
Differential_of_the_first_kind
Topics referred to by the same term
a cyclic group Cn, a classical root system cn (elliptic function), one of Jacobi's elliptic functions Carrier-to-noise ratio C/N, the signal-to-noise
CN
German polymath and scholar (1777–1855)
his work on elliptic function theory; however, Gauss cast his argument in a formal way that does not reveal its origin in elliptic function theory, and
Carl_Friedrich_Gauss
_{3}^{2}(0|\tau )} . The Neville theta functions are related to the Jacobi elliptic functions. If pq(u,m) is a Jacobi elliptic function (p and q are one of s,c,n,d)
Neville_theta_functions
Ratio of the perimeter of Bernoulli's lemniscate to its diameter
the lemniscate elliptic functions and is approximately equal to 2.62205755. It also appears in evaluation of the gamma and beta function at certain rational
Lemniscate_constant
Meromorphic function on the complex plane
An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory
L-function
Type of generalization of periodic functions in Euclidean space
automorphic functions can be seen as generalizations of modular forms (as therefore elliptic curves), constructed by some zeta function analogue on an
Automorphic_form
Paths of particles in the Schwarzschild solution to Einstein's field equations
particle in the Schwarzschild metric can be expressed in terms of elliptic functions. Samuil Kaplan in 1949 has shown that there is a minimum radius for
Schwarzschild_geodesics
Mathematical equation
It has two linearly independent solutions, called the periods of elliptic functions. The ratio of the two periods is equal to the period ratio τ, the
Picard–Fuchs_equation
Problem about mathematical number fields
the case of any imaginary quadratic field, by using modular functions and elliptic functions chosen with a particular period lattice related to the field
Hilbert's_twelfth_problem
Nonlinear and exact periodic wave solution of the Korteweg–de Vries equation
Korteweg–de Vries equation. These solutions are in terms of the Jacobi elliptic function cn, which is why they are coined cnoidal waves. They are used to describe
Cnoidal_wave
Theorem in complex analysis
theory of elliptic functions. In fact, it was Cauchy who proved Liouville's theorem. If f {\displaystyle f} is a non-constant entire function, then its
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Special function occurring in problems possessing elliptic symmetry
equation (PDE) boundary value problems possessing elliptic symmetry. In some usages, Mathieu function refers to solutions of the Mathieu differential equation
Mathieu_function
a relation between complete elliptic integrals, or as a relation between periods and quasiperiods of elliptic functions. The two forms are equivalent
Legendre's_relation
Topics referred to by the same term
(complexity), a class of computational complexity sl (elliptic function), sine lemniscate function Special linear group in mathematics, denoted SLn or SL(n)
SL
Conformal map projection
{2}}\operatorname {sl} \left(w\right)} is the lemniscatic sine function (see Lemniscate elliptic functions). According to Peirce, his projection has the following
Peirce_quincuncial_projection
Mathematical approximation of a function
)^{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
Taylor_series
Mathematical function of two positive real arguments
elliptic integrals, which are used, for example, in elliptic filter design. The arithmetic–geometric mean is connected to the Jacobi theta function θ
Arithmetic–geometric_mean
Modular unit in mathematics
mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions, or division
Elliptic_unit
Topics referred to by the same term
Protocol Symmetric group or Sn n-sphere or Sn sn (elliptic function), one of Jacobi's elliptic functions Sigma notation, also known as a summation SN, METAR
SN
Topics referred to by the same term
gamepads for PlayStation DeepSeek (chatbot) ds (elliptic function), one of Jacobi's elliptic functions De Sitter space (dS) Down syndrome, a genetic disorder
DS
Polynomials used in approximation theory
Jacobi elliptic modulus sn ( φ | κ ) {\displaystyle \operatorname {sn} (\varphi |\kappa )} is the Jacobi elliptic sine. The variation of the function within
Zolotarev_polynomials
Topics referred to by the same term
general-purpose, multi-paradigm programming language cs (elliptic function), one of Jacobi's elliptic functions Carbon steel Cirrostratus cloud Citizen science
CS
Type of differential operator
smooth functions (if the coefficients in the operator are smooth). Steady-state solutions to hyperbolic and parabolic equations generally solve elliptic equations
Elliptic_operator
coordinates of the varying point on this curve are given by the Jacobian elliptic functions. The Seiffert's spherical spiral can be expressed in cylindrical coordinates
Seiffert's_spiral
German mathematician (1815–1897)
attended the lectures of Christoph Gudermann and became interested in elliptic functions. In 1843 he taught in Deutsch Krone in West Prussia, and from 1848
Karl_Weierstrass
Fundamental trigonometric functions
elliptic functions Euler's formula Generalized trigonometry Hyperbolic function Lemniscate elliptic functions Law of sines List of periodic functions
Sine_and_cosine
French mathematician (1752–1833)
work on elliptic functions, including the classification of elliptic integrals, but it took Abel's study of the inverses of Jacobi's functions to solve
Adrien-Marie_Legendre
Topics referred to by the same term
Nameserver DOS Navigator, a DOS file manager dn (elliptic function), one of Jacobi's elliptic functions Dn, a Coxeter–Dynkin diagram Dn, a dihedral group
DN
Topics referred to by the same term
Stable Diffusion, a text-to-image generator sd (elliptic function), one of Jacobi's elliptic functions Standard deviation (SD), a statistical measure of
SD
Algebraic variety
"best models" can be very different from those taken directly from elliptic function theory. Hecke operators may be studied geometrically, as correspondences
Modular_curve
Mathematical method in elliptic functions
mapping of the parameters of an elliptic integral, useful for the efficient numerical evaluation of elliptic functions. It was originally due to John Landen
Landen's_transformation
Approach to public-key cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC
Elliptic-curve_cryptography
Norwegian mathematician (1802–1829)
years. He was also an innovator in the field of elliptic functions and the discoverer of Abelian functions. He made his discoveries while living in poverty
Niels_Henrik_Abel
Unicode block
P is a symbol for Weierstrass's elliptic function. It is officially aliased as U+2118 ℘ WEIERSTRASS ELLIPTIC FUNCTION. Variation selectors may be used
Mathematical Alphanumeric Symbols
Mathematical_Alphanumeric_Symbols
The zeta function of a mathematical operator O {\displaystyle {\mathcal {O}}} is a function defined as ζ O ( s ) = tr O − s {\displaystyle \zeta _{\mathcal
Zeta_function_(operator)
Class of partial differential equations
and G are functions of ( x , y ) {\displaystyle (x,y)} , using subscript notation for the partial derivatives. The PDE is called elliptic if B 2 − A
Elliptic partial differential equation
Elliptic_partial_differential_equation
Rational function of the form (az + b)/(cz + d)
R) important in the study of lattices in the complex plane, elliptic functions and elliptic curves. The discrete subgroups of PSL(2, R) are known as Fuchsian
Möbius_transformation
Function with a repeating pattern
}{k}}} . A function on the complex plane can have two distinct, incommensurate periods without being a constant function. The elliptic functions are a primary
Periodic_function
Topics referred to by the same term
the fourth generation of video game consoles cd (elliptic function), one of Jacobi's elliptic functions 400 (number), written CD in Roman numerals AD 400
CD_(disambiguation)
Topics referred to by the same term
personal luxury car Bitter SC, a luxury car sc (elliptic function), one of Jacobi's elliptic functions Scandium, symbol Sc, a chemical element Schmidt
SC
Topics referred to by the same term
(or "ns-2"), an open source network simulator ns (elliptic function), one of Jacobi's elliptic functions NS, the Néron–Severi group Nanosecond (abbreviated
NS
Type of mathematical function
as the error function and the elliptic integrals, were elementary functions of the second kind; their inverses, the elliptic functions, were considered
Elementary_function
)^{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
List_of_mathematical_series
Topics referred to by the same term
radioactivity, nuclear processes and nuclear properties nc (elliptic function), one of Jacobi's elliptic functions National coarse, a Unified Thread Standard for screws
NC
Something roughly the same as something else
mathematician Alfred Greenhill in 1892, in his book Applications of Elliptic Functions. Typical meanings of LaTeX symbols. ≈ {\displaystyle \approx } (\approx) :
Approximation
Projective variety that is also an algebraic group
early nineteenth century, the theory of elliptic functions succeeded in giving a basis for the theory of elliptic integrals, and this left open an obvious
Abelian_variety
Conductor–ground plane electrical transmission line
using elliptic integrals and jacobi elliptic functions. Smith uses the third fast Jacobi elliptic function estimation algorithm found in the elliptic functions
Microstrip
Way of defining a lattice in the complex plane
complex plane. This type of lattice is the underlying object with which elliptic functions and modular forms are defined. A fundamental pair of periods is a
Fundamental_pair_of_periods
Real function with secant line between points above the graph itself
corresponding norm. Some authors, such as refer to functions satisfying this inequality as elliptic functions. An equivalent condition is the following: f (
Convex_function
Topics referred to by the same term
and proposed dismantling of nuclear weapons nd (elliptic function), one of Jacobi's elliptic functions NADH dehydrogenase, an enzyme Non-distended, an
ND
Statistical lattice model with long-range interactions
pair potential ℘ ( z ) {\displaystyle \wp (z)} is the Weierstrass elliptic function, and σ → j {\displaystyle {\vec {\sigma }}_{j}} denotes the Pauli
Inozemtsev_model
Mathematical operation on points on an elliptic curve
Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic
Elliptic curve point multiplication
Elliptic_curve_point_multiplication
Conformal mappings in complex analysis
function. In the spherical case, that modular function is a rational function. For Euclidean triangles, the inverse can be expressed using elliptical
Schwarz_triangle_function
Unproved conjecture in mathematics
with an elliptic curve E {\displaystyle E} over a number field K {\displaystyle K} and the behaviour of its associated Hasse–Weil L-function L ( E , s
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Mathematical identities related to integer partitions
An elliptic function is a modular function if this function in dependence on the elliptic nome as an internal variable function results in a function, which
Rogers–Ramanujan_identities
Gauss sum on an elliptic curve
quartic residue symbol, and the exponential function in a Gauss sum is replaced by an elliptic function. They were introduced by Eisenstein (1850), at
Elliptic_Gauss_sum
Special function in the theory of elliptic functions
quarter periods K(m) and iK ′(m) are special functions that appear in the theory of elliptic functions. The quarter periods K and iK ′ are given by K
Quarter_period
German mathematician (1798–1852)
Weierstrass, who was greatly influenced by Gudermann's course on elliptic functions in 1839–1840, the first such course to be taught in any institute
Christoph_Gudermann
ratio Jacobi's elliptic functions Weierstrass's elliptic functions Theta function Elliptic modular function J-function Modular function Modular form Analytic
List of complex analysis topics
List_of_complex_analysis_topics
Indian mathematician (1887–1920)
Royal Society's history. He was elected "for his investigation in elliptic functions and the Theory of Numbers." On 13 October 1918, he was the first Indian
Srinivasa_Ramanujan
Elliptic curve used in Internet cryptography
an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed for use with the Elliptic-curve
Curve25519
the Weierstrass elliptic function. The coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } are given as elliptic functions of κ {\displaystyle
Somos_sequence
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION
ELLIPTIC FUNCTION