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WEIERSTRASS ELLIPTIC-FUNCTION

  • Weierstrass elliptic function
  • Class of mathematical functions

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

    Weierstrass elliptic function

    Weierstrass elliptic function

    Weierstrass_elliptic_function

  • Elliptic curve
  • Algebraic curve in mathematics

    type of equation is called a Weierstrass normal form, Weierstrass form, or Weierstrass equation. The definition of elliptic curve also requires that the

    Elliptic curve

    Elliptic curve

    Elliptic_curve

  • Weierstrass functions
  • 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

    Weierstrass functions

    Weierstrass_functions

  • Jacobi elliptic functions
  • Mathematical function

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

    Jacobi elliptic functions

    Jacobi_elliptic_functions

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

    Dixon elliptic functions

    Dixon elliptic functions

    Dixon_elliptic_functions

  • Elliptic function
  • Class of periodic mathematical functions

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

    Elliptic function

    Elliptic_function

  • Karl Weierstrass
  • German mathematician (1815–1897)

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

    Karl Weierstrass

    Karl Weierstrass

    Karl_Weierstrass

  • Lemniscate elliptic functions
  • Mathematical functions

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

    Lemniscate elliptic functions

    Lemniscate elliptic functions

    Lemniscate_elliptic_functions

  • J-invariant
  • 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

    J-invariant

    J-invariant

  • Gamma function
  • Extension of the factorial function

    theorem of the gamma function and investigated the connection between the gamma function and elliptic integrals. Karl Weierstrass further established the

    Gamma function

    Gamma function

    Gamma_function

  • Dedekind eta function
  • Mathematical function

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

    Dedekind eta function

    Dedekind_eta_function

  • List of mathematical functions
  • 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

  • Theta function
  • Special functions of several complex variables

    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

    Theta function

    Theta function

    Theta_function

  • Elliptic integral
  • 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

    Elliptic_integral

  • Doubly periodic function
  • 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

    Doubly_periodic_function

  • Pe
  • Topics referred to by the same term

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

    Pe

    Pe

  • Costa's minimal surface
  • Mathematical concept

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

    Costa's minimal surface

    Costa's minimal surface

    Costa's_minimal_surface

  • Modular form
  • Analytic function on the upper half-plane with a certain behavior under the modular group

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

    Modular form

    Modular_form

  • Sigma function
  • Topics referred to by the same term

    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

    Sigma function

    Sigma_function

  • List of things named after Karl Weierstrass
  • Weierstrass–Mandelbrot function Weierstrass approximation theorem Weierstrass coordinates Weierstrass's elliptic functions Weierstrass equation Weierstrass factorization

    List of things named after Karl Weierstrass

    List_of_things_named_after_Karl_Weierstrass

  • Modular lambda function
  • Symmetric holomorphic function

    }(-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}]}

    Modular lambda function

    Modular lambda function

    Modular_lambda_function

  • Riemann surface
  • One-dimensional complex manifold

    y)=(\wp (z),\wp '(z))} , where ℘ {\displaystyle \wp } is the Weierstrass elliptic function. Likewise, genus g {\displaystyle g} surfaces have Riemann surface

    Riemann surface

    Riemann surface

    Riemann_surface

  • Carl Gustav Jacob Jacobi
  • German mathematician (1804–1851)

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

    Carl Gustav Jacob Jacobi

    Carl Gustav Jacob Jacobi

    Carl_Gustav_Jacob_Jacobi

  • Complex multiplication
  • Theory of a class of elliptic curves

    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

    Complex multiplication

    Complex_multiplication

  • Delta function (disambiguation)
  • Topics referred to by the same term

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

    Delta function (disambiguation)

    Delta_function_(disambiguation)

  • Lamé function
  • Solutions of Lamé's equation

    where A and B are constants, and ℘ {\displaystyle \wp } is the Weierstrass elliptic function. The most important case is when B ℘ ( x ) = − κ 2 sn 2 ⁡ x

    Lamé function

    Lamé_function

  • List of periodic functions
  • 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

    List_of_periodic_functions

  • Weierstrass–Enneper parameterization
  • Construction for minimal surfaces

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

    Weierstrass–Enneper parameterization

    Weierstrass–Enneper parameterization

    Weierstrass–Enneper_parameterization

  • Picard–Fuchs equation
  • Mathematical equation

    and g 3 {\displaystyle g_{3}} the modular invariants of the elliptic curve in Weierstrass form: y 2 = 4 x 3 − g 2 x − g 3 . {\displaystyle y^{2}=4x^{3}-g_{2}x-g_{3}

    Picard–Fuchs equation

    Picard–Fuchs_equation

  • P (disambiguation)
  • Topics referred to by the same term

    of all primes and p an individual prime ℘-functions or p-functions, are the Weierstrass elliptic function p-series, a common name for the Harmonic series

    P (disambiguation)

    P_(disambiguation)

  • Gaussian function
  • Mathematical function

    and to define the Weierstrass transform. They are also abundantly used in quantum chemistry to form basis sets. Gaussian functions arise by composing

    Gaussian function

    Gaussian_function

  • Schwarzschild geodesics
  • Paths of particles in the Schwarzschild solution to Einstein's field equations

    {1}{r^{2}}}\right)}}}}.} This can be expressed in terms of the Weierstrass elliptic function ℘ {\textstyle \wp } . Unlike in classical mechanics, in Schwarzschild

    Schwarzschild geodesics

    Schwarzschild_geodesics

  • Harmonic function
  • Functions in mathematics

    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

    Harmonic function

    Harmonic function

    Harmonic_function

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

    Equianharmonic

    Equianharmonic

  • Fundamental pair of periods
  • Way of defining a lattice in the complex plane

    of as underlying many of the properties of elliptic functions (especially the Weierstrass elliptic function) and modular forms. The abelian group Z 2 {\displaystyle

    Fundamental pair of periods

    Fundamental pair of periods

    Fundamental_pair_of_periods

  • Transcendental function
  • Analytic function that does not satisfy a polynomial equation

    hyperbolic functions, and the inverses of all of these. Less familiar are the special functions of analysis, such as the gamma, elliptic, and zeta functions, all

    Transcendental function

    Transcendental_function

  • Mathematical Alphanumeric Symbols
  • Unicode block

    CAPITAL P is a symbol for Weierstrass's elliptic function. It is officially aliased as U+2118 ℘ WEIERSTRASS ELLIPTIC FUNCTION. Variation selectors may

    Mathematical Alphanumeric Symbols

    Mathematical_Alphanumeric_Symbols

  • Elliptic-curve cryptography
  • Approach to public-key cryptography

    its recommended elliptic-curve domain parameters to Special Publication 800-186. SP 800-186 includes previously recommended Weierstrass curves and two

    Elliptic-curve cryptography

    Elliptic-curve_cryptography

  • List of complex analysis topics
  • 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

  • Divisor function
  • Arithmetic function related to the divisors of an integer

    Fourier series of the Eisenstein series and the invariants of the Weierstrass elliptic functions. For k > 0 {\displaystyle k>0} , there is an explicit series

    Divisor function

    Divisor function

    Divisor_function

  • Script typeface
  • Class of typefaces inspired by handwriting

    (℘, ℘) (actually a misnomer, name is corrected into WEIERSTRASS ELLIPTIC FUNCTION) Antiqua (typeface class) Blackletter Chancery hand Record type

    Script typeface

    Script typeface

    Script_typeface

  • Letterlike Symbols
  • Unicode block

    Copyright 2117 ℘ ℘ {\displaystyle \wp } Script Capital P alias: Weierstrass Elliptic Function 2118 ℙ P {\displaystyle }\mathbb {P} Double-struck Capital P

    Letterlike Symbols

    Letterlike_Symbols

  • Pick's theorem
  • Formula for area of a grid polygon

    doubly periodic function related to Weierstrass elliptic functions. Applying the Poisson summation formula to the characteristic function of the polygon

    Pick's theorem

    Pick's theorem

    Pick's_theorem

  • Rank of an elliptic curve
  • Number of independent rational basis points with infinite order

    In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational

    Rank of an elliptic curve

    Rank_of_an_elliptic_curve

  • Legendre's relation
  • 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

    Legendre's relation

    Legendre's_relation

  • Nome (mathematics)
  • 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)

    Nome_(mathematics)

  • Elliptic unit
  • 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

    Elliptic_unit

  • Pi
  • Number, approximately 3.14

    {5}{2}}{\bigr )}={\tfrac {3}{4}}{\sqrt {\pi }}} . The gamma function is defined by its Weierstrass product development: Γ ( z ) = e − γ z z ∏ n = 1 ∞ e z /

    Pi

    Pi

  • Euler's three-body problem
  • Problem in physics and astronomy

    full three dimensional case, can be expressed in terms of Weierstrass's elliptic functions For convenience, the problem may also be solved by numerical

    Euler's three-body problem

    Euler's_three-body_problem

  • Ahlfors theory
  • Mathematical theory

    f(z) = ℘(Kz), where K > 0 is arbitrarily large, and ℘ is the Weierstrass elliptic function satisfying the differential equation ( ℘ ′ ) 2 = 4 ( ℘ − e 1

    Ahlfors theory

    Ahlfors_theory

  • Laplace's equation
  • Second-order partial differential equation

    Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. Laplace's equation is also a special case

    Laplace's equation

    Laplace's equation

    Laplace's_equation

  • Hyperelliptic curve
  • 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

    Hyperelliptic curve

    Hyperelliptic_curve

  • Elliptic curve point multiplication
  • 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

  • Christoph Gudermann
  • German mathematician (1798–1852)

    1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and

    Christoph Gudermann

    Christoph_Gudermann

  • Elliptic curve only hash
  • Cryptographic hash function

    The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in

    Elliptic curve only hash

    Elliptic_curve_only_hash

  • Lenstra elliptic-curve factorization
  • Algorithm for integer factorization

    x P {\displaystyle b=y_{P}^{2}-x_{P}^{3}-ax_{P}} . The elliptic curve E is then in Weierstrass form given by y 2 = x 3 + a x + b {\displaystyle y^{2}=x^{3}+ax+b}

    Lenstra elliptic-curve factorization

    Lenstra_elliptic-curve_factorization

  • Differential of the first kind
  • 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,

    Differential of the first kind

    Differential_of_the_first_kind

  • Unicode alias names and abbreviations
  • Names and aliases of Unicode characters

    CAPITAL P is actually a lowercase p, and so is given alias name ※ WEIERSTRASS ELLIPTIC FUNCTION: "actually this has the form of a lowercase calligraphic p,

    Unicode alias names and abbreviations

    Unicode_alias_names_and_abbreviations

  • Genus g surface
  • Smooth closed surface with g holes

    projective plane follows naturally from a property of Weierstrass's elliptic functions that allows elliptic curves to be obtained from the quotient of the complex

    Genus g surface

    Genus_g_surface

  • Bernhard Riemann
  • German mathematician (1826–1866)

    Otherwise, Weierstrass was very impressed with Riemann, especially with his theory of abelian functions. When Riemann's work appeared, Weierstrass withdrew

    Bernhard Riemann

    Bernhard Riemann

    Bernhard_Riemann

  • Inozemtsev model
  • Statistical lattice model with long-range interactions

    where the pair potential ℘ ( z ) {\displaystyle \wp (z)} is the Weierstrass elliptic function, and σ → j {\displaystyle {\vec {\sigma }}_{j}} denotes the

    Inozemtsev model

    Inozemtsev_model

  • Modular curve
  • Algebraic variety

    in the following table. As elliptic curves over Q {\displaystyle \mathbb {Q} } , they have minimal, integral Weierstrass models y 2 + a 1 x y + a 3 y

    Modular curve

    Modular_curve

  • Somos sequence
  • denotes the Weierstrass elliptic function. The coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } are given as elliptic functions of κ {\displaystyle

    Somos sequence

    Somos_sequence

  • Orchard-planting problem
  • Geometry; how many 3-point lines can n points form

    Grünbaum, and Sloane (1974), using a construction based on Weierstrass's elliptic functions. An elementary construction using hypocycloids was found by

    Orchard-planting problem

    Orchard-planting problem

    Orchard-planting_problem

  • Conductor of an elliptic curve
  • In mathematics, the conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal

    Conductor of an elliptic curve

    Conductor_of_an_elliptic_curve

  • E (mathematical constant)
  • 2.71828...; base of natural logarithms

    methods based on elliptic functions and fast convergence of the AGM and Newton's method can be used to compute the exponential function. The digit expansion

    E (mathematical constant)

    E (mathematical constant)

    E_(mathematical_constant)

  • Eisenstein series
  • Series representing modular forms

    k {\displaystyle d_{k}} occur in the series expansion for Weierstrass's elliptic functions: ℘ ( z ) = 1 z 2 + z 2 ∑ k = 0 ∞ d k z 2 k k ! = 1 z 2 + ∑

    Eisenstein series

    Eisenstein_series

  • Hölder condition
  • Type of continuity of a complex-valued function

    It does not satisfy a Hölder condition of any order, however. The Weierstrass function defined by: f ( x ) = ∑ n = 0 ∞ a n cos ⁡ ( b n π x ) , {\displaystyle

    Hölder condition

    Hölder_condition

  • Picard theorem
  • Theorem about the range of an analytic function

    punctured plane by the unit disc. This function is explicitly constructed in the theory of elliptic functions. If f {\textstyle f} omits two values, then

    Picard theorem

    Picard theorem

    Picard_theorem

  • Sergei Bernstein
  • Soviet mathematician

    (approximation theory) Bernstein's theorem on monotone functions Bernstein–von Mises theorem Stone–Weierstrass theorem Youschkevitch, A. P. "BERNSTEIN, SERGEY

    Sergei Bernstein

    Sergei_Bernstein

  • Mordell–Weil group
  • Abelian group

    the case of a specific elliptic curve E / Q {\displaystyle E/\mathbb {Q} } . Let E {\displaystyle E} be defined by the Weierstrass equation y 2 = x ( x

    Mordell–Weil group

    Mordell–Weil_group

  • Weil pairing
  • Binary function non degenerative defined between the point of twist of an abelian variety

    corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function. Choose an elliptic curve E defined

    Weil pairing

    Weil_pairing

  • Genus–degree formula
  • Theorem in classical algebraic geometry

    {1}{2}}r(r-1)} . Elliptic curves are parametrized by Weierstrass elliptic functions. Since these parameterizing functions are doubly periodic, the elliptic curve

    Genus–degree formula

    Genus–degree_formula

  • Algebraic curve
  • Curve defined as zeros of polynomials

    a_{1}=a_{2}=a_{3}=0,} which gives the classical Weierstrass form y 2 = x 3 + p x + q . {\displaystyle y^{2}=x^{3}+px+q.} Elliptic curves carry the structure of an abelian

    Algebraic curve

    Algebraic curve

    Algebraic_curve

  • Quasilinearization
  • Technique in mathematics

    solution of the differential equation can be expressed using the Weierstrass elliptic function ℘, like so: y ( x ) = 6 ℘ ( x − α | 0 , β ) {\displaystyle y(x)=6\wp

    Quasilinearization

    Quasilinearization

    Quasilinearization

  • Moduli stack of elliptic curves
  • Algebraic stack in mathematics

    {C} /\Lambda } into P 2 {\displaystyle \mathbb {P} ^{2}} from the Weierstrass P function pg 165. This isomorphic correspondence ϕ : C / Λ → E ( C ) {\displaystyle

    Moduli stack of elliptic curves

    Moduli_stack_of_elliptic_curves

  • Montgomery curve
  • Type of elliptic curve

    Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain

    Montgomery curve

    Montgomery_curve

  • Scientific phenomena named after people
  • Weierstrass–Casorati theorem – Karl Theodor Wilhelm Weierstrass and Felice Casorati Weierstrass's elliptic functions, factorization theorem, function

    Scientific phenomena named after people

    Scientific_phenomena_named_after_people

  • Uniform convergence
  • Mode of convergence of a function sequence

    of his proofs. Later Gudermann's pupil, Karl Weierstrass, who attended his course on elliptic functions in 1839–1840, coined the term gleichmäßig konvergent

    Uniform convergence

    Uniform convergence

    Uniform_convergence

  • Cubic plane curve
  • Type of mathematical curve

    x3 Graph of a cubic function Cusp at infinity Witch of Agnesi Isolated point at infinity on the y-axis y(x2 + a2) = a3 Elliptic cubics One projective

    Cubic plane curve

    Cubic plane curve

    Cubic_plane_curve

  • Exact solutions of classical central-force problems
  • {a}{r^{2}}}+cr} , the problem also is solved explicitly in terms of Weierstrass elliptic functions. Whittaker, pp. 80–95. Izzo and Biscani Whittaker ET (1937)

    Exact solutions of classical central-force problems

    Exact_solutions_of_classical_central-force_problems

  • Mollifier
  • Integration kernels for smoothing out sharp features

    Generalized function Kurt Otto Friedrichs Non-analytic smooth function Sergei Sobolev Weierstrass transform That is, the mollified function is close to

    Mollifier

    Mollifier

    Mollifier

  • Unicode character property
  • Unicode code point property names and their uses

    CAPITAL P is actually a lowercase p, and so is given alias name WEIERSTRASS ELLIPTIC FUNCTION: "actually this has the form of a lowercase calligraphic p,

    Unicode character property

    Unicode_character_property

  • Projective variety
  • Algebraic variety in a projective space

    abelian variety of dimension 1, i.e., from an elliptic curve. In fact, the Weierstrass's elliptic function ℘ {\displaystyle \wp } attached to L satisfies

    Projective variety

    Projective variety

    Projective_variety

  • Liouville's theorem (complex analysis)
  • 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)

    Liouville's_theorem_(complex_analysis)

  • Glossary of real and complex analysis
  • a generalized function that is a solution of a differential equation. Weierstrass 1.  Weierstrass preparation theorem. 2.  Weierstrass M-test. Weitzenböck

    Glossary of real and complex analysis

    Glossary_of_real_and_complex_analysis

  • Timeline of abelian varieties
  • problem in genus 2. c. 1850 Thomas Weddle - Weddle surface 1856 Weierstrass elliptic functions 1857 Bernhard Riemann lays the foundations for further work

    Timeline of abelian varieties

    Timeline_of_abelian_varieties

  • Gaussian filter
  • Filter in electronics and signal processing

    input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. The one-dimensional Gaussian filter

    Gaussian filter

    Gaussian filter

    Gaussian_filter

  • List of number theory topics
  • related to pi Squaring the circle Proof that e is irrational Lindemann–Weierstrass theorem Hilbert's seventh problem Gelfond–Schneider theorem Erdős–Borwein

    List of number theory topics

    List_of_number_theory_topics

  • Function of several complex variables
  • Type of mathematical functions

    principle, inverse function theorem, and implicit function theorems also hold. The Weierstrass preparation theorem serves as an implicit function theorem for

    Function of several complex variables

    Function_of_several_complex_variables

  • Leopold Kronecker
  • German mathematician (1823–1891)

    formulation of a continuous, nowhere differentiable function by his colleague, Karl Weierstrass. Also named for Kronecker are the Kronecker limit formula

    Leopold Kronecker

    Leopold Kronecker

    Leopold_Kronecker

  • Painlevé transcendents
  • Special functions in mathematics

    derivative) with the Painlevé property can be transformed into the Weierstrass elliptic equation or the Riccati equation, all of which can be solved explicitly

    Painlevé transcendents

    Painlevé_transcendents

  • List of things named after Carl Friedrich Gauss
  • as Weierstrass transform. Gauss–Lucas theorem Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions Gauss's

    List of things named after Carl Friedrich Gauss

    List of things named after Carl Friedrich Gauss

    List_of_things_named_after_Carl_Friedrich_Gauss

  • List of algebraic geometry topics
  • theorem Twisted cubic Elliptic curve, cubic curve Elliptic function, Jacobi's elliptic functions, Weierstrass's elliptic functions Elliptic integral Complex

    List of algebraic geometry topics

    List_of_algebraic_geometry_topics

  • Imaginary hyperelliptic curve
  • Type of algebraic curve

    \operatorname {div} (f)=2nP-2nO} if P {\displaystyle P} is a Weierstrass point. For elliptic curves the Jacobian turns out to simply be isomorphic to the

    Imaginary hyperelliptic curve

    Imaginary_hyperelliptic_curve

  • Eric Harold Neville
  • English mathematician

    Jacobian Elliptic Functions (1944). By starting with the Weierstrass p-function and associating with it a group of doubly periodic functions with two

    Eric Harold Neville

    Eric_Harold_Neville

  • Ferdinand Georg Frobenius
  • German mathematician (1849–1917)

    mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is

    Ferdinand Georg Frobenius

    Ferdinand Georg Frobenius

    Ferdinand_Georg_Frobenius

  • Abramowitz and Stegun
  • 1964 mathematical reference work edited by M. Abramowitz and I. Stegun

    Hypergeometric Functions Coulomb Wave Functions Hypergeometric Functions Jacobian Elliptic Functions and Theta Functions Elliptic Integrals Weierstrass Elliptic and

    Abramowitz and Stegun

    Abramowitz and Stegun

    Abramowitz_and_Stegun

  • Boris Bukreev
  • Russian and Soviet mathematician

    Karl Weierstrass's theory of elliptic functions. This became a topic of his Master's thesis titled "On the expansion of transcendental function in partial

    Boris Bukreev

    Boris Bukreev

    Boris_Bukreev

  • Fractal
  • Infinitely detailed mathematical structure

    but not differentiable functions in the 19th century by the seminal work of Bernard Bolzano, Bernhard Riemann, and Karl Weierstrass, and on to the coining

    Fractal

    Fractal

    Fractal

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  • Fuller
  • Surname or Lastname

    English

    Fuller

    English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.

    Fuller

  • Genki
  • Boy/Male

    Buddhist, Indian, Japanese

    Genki

    Mysterious Function

    Genki

  • KHEN-TA
  • Male

    Egyptian

    KHEN-TA

    , Functionary of the Interior.

    KHEN-TA

  • KAFH-EN-MA-NOFRE
  • Male

    Egyptian

    KAFH-EN-MA-NOFRE

    , a high Egyptian functionary.

    KAFH-EN-MA-NOFRE

  • Jenner
  • Surname or Lastname

    English (chiefly Kent and Sussex)

    Jenner

    English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.

    Jenner

  • Catt
  • Surname or Lastname

    English

    Catt

    English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.

    Catt

  • ANIEI
  • Male

    Egyptian

    ANIEI

    , an Egyptian functionary.

    ANIEI

  • ANKHSNEF
  • Male

    Egyptian

    ANKHSNEF

    , an Egyptian functionary.

    ANKHSNEF

  • AMENHERATF
  • Male

    Egyptian

    AMENHERATF

    , the son of the functionary Heknofre.

    AMENHERATF

  • Douthit
  • Surname or Lastname

    English

    Douthit

    English : variant of Douthwaite, a habitational name from Dowthwaite in Cumbria or Dowthwaite Hall in North Yorkshire. The first is from the Old Norse personal name Dúfa + Old Norse þveit ‘clearing’; the second is from the Old Irish personal name Dubhan + Old Norse þveit. The elliptic form of the surname probably reflects the local pronunciation of the place names.

    Douthit

  • VIRIDOMARUS
  • Male

    Celtic

    VIRIDOMARUS

    , great justiciary, or functionary.

    VIRIDOMARUS

  • Gates
  • Surname or Lastname

    English

    Gates

    English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.

    Gates

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  • Biblical

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  • Vickers
  • Surname or Lastname

    English

    Vickers

    English : patronymic for the son of a vicar or, perhaps in most cases, an occupational name for the servant of a vicar (see Vicker). In many cases it may represent an elliptical form of a topographic name. Compare Parsons.

    Vickers

  • ASESKAFANKH
  • Male

    Egyptian

    ASESKAFANKH

    , a great functionary.

    ASESKAFANKH

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Online names & meanings

  • Yogitha | யோகீதா
  • Girl/Female

    Tamil

    Yogitha | யோகீதா

    One who can concentrate or female disciple or enchanted

  • Brian
  • Male

    English

    Brian

    High, Noble, Strong

  • Srikrishna
  • Boy/Male

    Bengali, Hindu, Indian, Sanskrit, Telugu

    Srikrishna

    Lord Krishna

  • Marylu
  • Girl/Female

    English Hebrew

    Marylu

    Derived from Mary, meaning bitter. Mary was the biblical mother of Christ.

  • Thornell
  • Surname or Lastname

    Swedish

    Thornell

    Swedish : ornamental name composed of the elements thorn, an ornamental spelling of torn ‘thorn bush’ + the common adjectival suffix -ell, from Latin -elius.English : variant of Thornhill.

  • Amadis
  • Girl/Female

    Latin

    Amadis

    Loved by God.

  • NOAH
  • Male

    English

    NOAH

    Anglicized form of Greek Noe (Hebrew Noach), NOAH means "rest." In the bible, this is the name of the last antediluvian patriarch, the main character of the flood story. Compare with feminine Noah.

  • Debashmeet
  • Boy/Male

    Hindu, Indian

    Debashmeet

    Lord of the Rings

  • Udyot | உத்யோத
  • Boy/Male

    Tamil

    Udyot | உத்யோத

    Shining

  • Sigismund
  • Boy/Male

    German Teutonic

    Sigismund

    Victorious defender.

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Other words and meanings similar to

WEIERSTRASS ELLIPTIC-FUNCTION

AI search in online dictionary sources & meanings containing WEIERSTRASS ELLIPTIC-FUNCTION

WEIERSTRASS ELLIPTIC-FUNCTION

  • Ecliptic
  • a.

    Pertaining to the ecliptic; as, the ecliptic way.

  • Elliptic-lanceolate
  • a.

    Having a form intermediate between elliptic and lanceolate.

  • Ecliptic
  • a.

    A great circle of the celestial sphere, making an angle with the equinoctial of about 23¡ 28'. It is the apparent path of the sun, or the real path of the earth as seen from the sun.

  • Ellipsis
  • n.

    An ellipse.

  • Elliptic
  • a.

    Alt. of Elliptical

  • Elliptical
  • a.

    Having a part omitted; as, an elliptical phrase.

  • Ellipse
  • n.

    The elliptical orbit of a planet.

  • Sign
  • n.

    The twelfth part of the ecliptic or zodiac.

  • Oval
  • a.

    Broadly elliptical.

  • Elliptical
  • a.

    Of or pertaining to an ellipse; having the form of an ellipse; oblong, with rounded ends.

  • Pelta
  • n.

    A small shield, especially one of an approximately elliptic form, or crescent-shaped.

  • Mellitic
  • a.

    Pertaining to, or derived from, the mineral mellite.

  • Mellic
  • a.

    See Mellitic.

  • Latitude
  • n.

    The angular distance of a heavenly body from the ecliptic.

  • Mellitic
  • a.

    Containing saccharine matter; marked by saccharine secretions; as, mellitic diabetes.

  • Ellipse
  • n.

    Omission. See Ellipsis.

  • Ecliptic
  • a.

    A great circle drawn on a terrestrial globe, making an angle of 23¡ 28' with the equator; -- used for illustrating and solving astronomical problems.

  • Mellitate
  • n.

    A salt of mellitic acid.

  • Ecliptic
  • a.

    Pertaining to an eclipse or to eclipses.

  • Ellipses
  • pl.

    of Ellipsis