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mathematics, the Jacobi transform is an integral transform named after the mathematician Carl Gustav Jacob Jacobi, which uses Jacobi polynomials P n α
Jacobi_transform
German mathematician (1804–1851)
Carl Gustav Jacob Jacobi (/jɑːˈkoʊbiˌ dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental
Carl_Gustav_Jacob_Jacobi
Hankel transform Hartley transform Hermite transform Hilbert transform Hilbert–Schmidt integral operator Jacobi transform Laguerre transform Laplace
List_of_transforms
Jacobi set Jacobi sum Jacobi symbol Jacobi theta function Jacobi zeta function Jacobi's theorem (skew-symmetric matrix) Jacobi transform Jacobi triple product
List of things named after Carl Gustav Jacob Jacobi
List_of_things_named_after_Carl_Gustav_Jacob_Jacobi
P_{n}(x)} as kernels of the transform. Legendre transform is a special case of Jacobi transform. The Legendre transform of a function f ( x ) {\displaystyle
Legendre transform (integral transform)
Legendre_transform_(integral_transform)
Mapping involving integration between function spaces
In mathematics, an integral transform is a type of transformation that maps a function from its original function space into another function space via
Integral_transform
Integral transform useful in probability theory, physics, and engineering
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable
Laplace_transform
Function in discrete mathematics
In mathematics, the discrete Fourier transform (DFT) is a discrete version of the Fourier transform that converts a finite sequence of numbers into another
Discrete_Fourier_transform
Special functions of several complex variables
)^{4}} which is the Fermat curve of degree four. Jacobi's identities describe how theta functions transform under the modular group, which is generated by
Theta_function
Formulation of classical mechanics
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics
Hamilton–Jacobi_equation
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
Square matrix in which each ascending skew-diagonal from left to right is constant
B_{n}} is the Hankel transform of the sequence b k . {\displaystyle b_{k}.} The Hankel transform is invariant under the binomial transform of a sequence. That
Hankel_matrix
1976 BBC television series
its 1935 sequel Claudius the God. Written by Jack Pulman, it stars Derek Jacobi as Claudius, with Siân Phillips, Brian Blessed, George Baker, Margaret Tyzack
I,_Claudius_(TV_series)
Linear operator
A Jacobi operator, also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix. It
Jacobi_operator
Family of linear transformations
vector space, satisfying the axioms of bilinearity, alternatization, and the Jacobi identity. Here the operation [ , ] is the commutator which satisfies all
Lorentz_transformation
Matrix of partial derivatives of a vector-valued function
referred to simply as the Jacobian. They are named after Carl Gustav Jacob Jacobi (1804-1851). The Jacobian matrix is the natural generalization of the derivative
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
French polymath (1749–1827)
Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he
Pierre-Simon_Laplace
Transforms equations for numerical solution
size) to the cost of multiplication of A {\displaystyle A} by a vector. The Jacobi preconditioner is one of the simplest forms of preconditioning, in which
Preconditioner
37–99. 2008. Vanessa A. Baird; Tonja Jacobi. "How the Dissent Becomes the Majority: Using Federalism to Transform Coalitions in the U.S. Supreme Court"
Tonja_Jacobi
Generalization of beta distribution
density is expressed by a Jacobi polynomial. The distribution of the largest eigenvalue is well approximated by a transform of the Tracy–Widom distribution
Matrix variate beta distribution
Matrix_variate_beta_distribution
British drama television series
BBC One on 20 November 2012 until 15 March 2020. The series stars Derek Jacobi and Anne Reid as Alan and Celia, two widowed old aged pensioners (OAPs)
Last_Tango_in_Halifax
Kind of square matrix in linear algebra
)U_{(n-2)}^{*}=U_{(n-2)}\dots U_{2}U_{1}A(U_{(n-2)}\dots U_{2}U_{1})^{*}=UAU^{*}} . A Jacobi rotation (also called Givens rotation) is an orthogonal matrix transformation
Hessenberg_matrix
2005 film by Kirk Jones
screenplay) as Nanny McPhee, along with Colin Firth, Kelly Macdonald, Derek Jacobi, Celia Imrie, Patrick Barlow, Imelda Staunton, Thomas Sangster and Angela
Nanny_McPhee
Character in TV series Doctor Who
Master has been portrayed by Derek Jacobi, John Simm, Michelle Gomez, and Sacha Dhawan. Beevers, Roberts, Jacobi, Simm, Gomez, and Dhawan have reprised
The_Master_(Doctor_Who)
Norwegian mathematician (1842–1899)
W-curve Carathéodory–Jacobi–Lie theorem Lie algebra Lie bracket Lie group Lie product formula Lie sphere geometry Lie theory Lie transform Lie's theorem Lie's
Sophus_Lie
Real square matrix whose columns and rows are orthogonal unit vectors
uniquely) in terms of the three angles used, often called Euler angles. A Jacobi rotation has the same form as a Givens rotation, but is used to zero both
Orthogonal_matrix
Special function in mathematics
{\displaystyle \operatorname {Re} (a)>0.} (This integral can be viewed as a Mellin transform.) The formula can be obtained, roughly, by writing ζ ( s , a ) Γ ( s )
Hurwitz_zeta_function
Complex-differentiable part of a Maass wave function
indefinite lattices of dimension 2, and to Appell–Lerch sums, and to meromorphic Jacobi forms. Zwegers's fundamental result shows that mock theta functions are
Mock_modular_form
Property of mathematical knots
number of chords in the Chord diagram transformed from the Jacobi diagram. Just like for the tangles, the Jacobi diagrams form a monoidal category with
Kontsevich_invariant
Taylor Siméon Denis Poisson Hermann Schwarz Camille Jordan Carl Gustav Jacob Jacobi Eugène Rouché Gerardus Mercator Joseph Liouville Pierre-Simon Laplace August
List of complex analysis topics
List_of_complex_analysis_topics
Concept in linear algebra
sparse matrices, and/or parallel machines. Block reflector Givens rotation Jacobi rotation Householder, A. S. (1958). "Unitary Triangularization of a Nonsymmetric
Householder_transformation
German park
with parterre and avenue. In the 1770s, his son Friedrich Heinrich Jacobi transformed the Baroque garden into an English landscape garden, preserving the
Malkastenpark
Polynomial sequence
useful to reveal recurrences, to demonstrate that they are special cases of Jacobi polynomials, to write down the differential equations, etc.: R n m ( ρ )
Zernike_polynomials
Measure defined on all open sets of a topological space
The theorem is named after Harald Cramér and Herman Ole Andreas Wold. Jacobi operator D. H. Fremlin, 2000. Measure Theory Archived 2010-11-01 at the
Borel_measure
Norwegian mathematician (1802–1829)
to Crelle's Journal. But in mid-1828 he published, in rivalry with Carl Jacobi, an important work on elliptic functions in Astronomische Nachrichten in
Niels_Henrik_Abel
Number, approximately 3.14
constant π is the unique constant making the Jacobi theta function an automorphic form, meaning that it transforms in a specific way. Certain identities hold
Pi
Rejection of certain ideas about reality
particularly in Germany and Russia through the works of Friedrich Heinrich Jacobi and Ivan Turgenev. It took center stage in the thought of Friedrich Nietzsche
Nihilism
Country in South Asia
certainly I have never met his equal, and I can compare him only with Euler and Jacobi. He worked, far more than the majority of modern mathematicians, by induction
India
Jain manuscript written by Bhadrabahu
the lineage of mendicants who followed Mahavir. Neminatha Parshvanatha Jacobi, Hermann (1884). Müller, F. Max (ed.). Kalpa Sutra, Jain Sutras Part I,
Kalpa_Sūtra
Property of certain dynamical systems
Hamilton–Jacobi method, in which solutions to Hamilton's equations are sought by first finding a complete solution of the associated Hamilton–Jacobi equation
Integrable_system
Equivalence under a change of basis (linear algebra)
T=P^{-1}SP} . The transform in the original basis is found to be the product of three easy-to-derive matrices. In effect, the similarity transform operates in
Matrix_similarity
Characters in a DC Comics series
acting as superheroes. Moloch the Mystic (real name Edgar William "Eddie" Jacobi, also known as Edgar William Vaughn, and William Edgar Bright) is a crime
List_of_Watchmen_characters
Concept in physics and mathematics
In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion
Galilean_transformation
Matrix decomposition
of the columns of the transformed matrix M {\displaystyle M} . Two-sided Jacobi SVD algorithm—a generalization of the Jacobi eigenvalue algorithm—is
Singular_value_decomposition
Mathematical function
themselves allow the construction of generalizations of the Jacobi theta function which transform under the modular group; this is what leads to the identities
Dedekind_eta_function
American mathematician
S. C. (1996). "New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function". Proceedings of the National
Stephen_Milne_(mathematician)
1973 thriller film directed by Fred Zinnemann
It stars Edward Fox as the title character, with Michael Lonsdale, Derek Jacobi, Terence Alexander, Michel Auclair, Alan Badel, Donald Sinden, Tony Britton
The_Day_of_the_Jackal_(film)
Fantasy comedy TV series (2019–2026)
that also includes Jon Hamm, Miranda Richardson, Michael McKean, Derek Jacobi, Brian Cox, Benedict Cumberbatch, and Frances McDormand as the voice of
Good_Omens_(TV_series)
Burgers' equation Euler equations Fokker–Planck equation Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation Heat equation Laplace's equation Laplace operator
List of partial differential equation topics
List_of_partial_differential_equation_topics
Abel's identity Abel's inequality Abel's irreducibility theorem Abel–Jacobi map Abel–Jacobi theorem Abel polynomials Abel's summation formula Abelian means
List of things named after Niels Henrik Abel
List_of_things_named_after_Niels_Henrik_Abel
English mathematician, mathematical physicist (born 1931)
Penrose–Hawking singularity theorems Penrose graphical notation Penrose transform Penrose–Terrell effect pp-wave spacetime Schrödinger–Newton equations
Roger_Penrose
2015 film by Kenneth Branagh
Blanchett, Richard Madden, Stellan Skarsgård, Holliday Grainger, Derek Jacobi, and Helena Bonham Carter. Development for Cinderella began in May 2010
Cinderella (2015 American film)
Cinderella_(2015_American_film)
British artist (born 1965)
series of portraits of Kenneth Branagh, Judi Dench, Adrian Lester, Derek Jacobi and Lily James. Newley worked on the portraits for a year, and was granted
Alexander_Newley
Portuguese-Dutch philosopher (1632–1677)
for Jacobi, was the result of Enlightenment rationalism, and it would finally end in absolute atheism. Moses Mendelssohn disagreed with Jacobi, saying
Baruch_Spinoza
chain rule method (calculus) Inverse transform sampling method (probability) Iterative method (numerical analysis) Jacobi method (linear algebra) Largest remainder
List of mathematics-based methods
List_of_mathematics-based_methods
Interpretation of quantum mechanics
the Hamiltonian, in the second Hamilton-Jacobi equation is now obtained using a second order Legendre transform. Moreover, due to the divergent part of
Stochastic_quantum_mechanics
Two interrelated physics theories by Albert Einstein
cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding
Theory_of_relativity
complex-affine transforms, we only permit real-affine transforms, then there are 2 more families: twisted Hermite, and twisted Jacobi: The 2 extra cases
Bochner's theorem (orthogonal polynomials)
Bochner's_theorem_(orthogonal_polynomials)
Scottish actor (1949–1990)
Television Shakespeare films: as Fortinbras in Hamlet (1980) starring Derek Jacobi; the protagonist Bertram in the acclaimed production of All's Well That
Ian_Charleson
Organ central to the nervous system
PMID 36048944. Tosches, Maria Antonietta; Yamawaki, Tracy M.; Naumann, Robert K.; Jacobi, Ariel A.; Tushev, Georgi; Laurent, Gilles (2018-05-25). "Evolution of pallium
Brain
Formulation of classical mechanics using momenta
mechanics Dynamical systems theory Hamiltonian system Hamilton–Jacobi equation Hamilton–Jacobi–Einstein equation Lagrangian mechanics Maxwell's equations
Hamiltonian_mechanics
Hungarian and American mathematician and physicist (1903–1957)
analysis, although implicitly. He was also one of the first to write about the Jacobi method. At Los Alamos, he wrote several classified reports on solving problems
John_von_Neumann
Simple model for one-dimensional crystal in solid-state physics
Toda lattice can be solved by virtue of the inverse scattering transform for the Jacobi operator L. The main result implies that arbitrary (sufficiently
Toda_lattice
Specialty in philosophy, focused on German language origin
atheism dispute, Jacobi further explicated his view that the Enlightenment and philosophy led to nihilism, popularizing the concept. Jacobi advocated fideism
German_philosophy
1913–1927 novel in seven volumes by Marcel Proust
Timberlake Wertenbaker and broadcast on BBC Radio 4 in 2019, with Derek Jacobi as the narrator. Andy Warhol's 1955 book A La Recherche du Shoe Perdu marked
In_Search_of_Lost_Time
Overview of mechanics based on the least action principle
the transformation is not canonical. The Hamilton–Jacobi equation By setting the canonically transformed Hamiltonian K = 0, and the type-2 generating function
Analytical_mechanics
American cardiologist (1929–2026)
cardiologist. He was a “groundbreaking cardiologist whose research helped transform heart disease from a near-certain killer into a condition often manageable
Eugene_Braunwald
Medical condition
1111/j.1600-0047.2004.00327.x. PMID 15128384. S2CID 24499847. Wittchen HU, Jacobi F (August 2005). "Size and burden of mental disorders in Europe—a critical
Mental_disorder
Mathematical theorem
theory of modular forms is the theta representation, so named because the Jacobi theta function is invariant under the action of the discrete subgroup of
Stone–von_Neumann_theorem
Greek mythological creature
Great Britain. London: Typis Rogeri Norton, impensis Johannis Martin, & Jacobi Allestrye. p. 129. Retrieved March 30, 2026. National Gallery of Art, Washington
Centaur
1994 film by Fred Schepisi
Walters Meg Ryan as Catherine Boyd Walter Matthau as Albert Einstein Lou Jacobi as Kurt Gödel Gene Saks as Boris Podolsky Joseph Maher as Nathan Liebknecht
I.Q._(film)
Physician that treated patients with bubonic plague
mask of some form since at least 1373, when Johannes Jacobi recommended the use of masks, but Jacobi gives no physical description of the masks. There is
Plague_doctor
Philosophical movement
influential figure of the movement. Other thinkers, such as Friedrich Heinrich Jacobi, Karl Leonhard Reinhold, Friedrich Schlegel, and Novalis, also made major
German_idealism
Fundamental solution to the heat equation, given boundary values
simplest cases of a disc or square involve, respectively, Bessel functions and Jacobi theta functions. Nevertheless, the heat kernel still exists and is smooth
Heat_kernel
Class of mathematical functions
e_{3}} are the three roots described above and where the modulus k of the Jacobi functions equals k = e 2 − e 3 e 1 − e 3 {\displaystyle k={\sqrt {\frac
Weierstrass_elliptic_function
English actor, playwright and theatre director (born 1960)
identity crisis), which toured England in 2007. On 8 September 2007 Derek Jacobi and Rylance unveiled a Declaration of Reasonable Doubt on the authorship
Mark_Rylance
Analytic function in mathematics
Philippe; Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bulletin of
Riemann_zeta_function
Physics problem related to laws of motion and gravity
problem has a 4-dimensional phase space, but only one conserved quantity, the Jacobi integral. It was shown by Heinrich Bruns that there are no more algebraic
Three-body_problem
Gives conditions for the solvability of quadratic equations modulo prime numbers
next Article he generalizes this to what are basically the rules for the Jacobi symbol (below). Letting A, A′, etc. represent any (prime or composite) positive
Quadratic_reciprocity
Ancient Greek deity and herald of the gods
Reflections of the Soul. Open Court Publishing, 1985. ISBN 0-87548-417-4. Jacobi, M. (1907). Catholic Encyclopedia: "Astrology" Archived 21 July 2017 at
Hermes
German-born theoretical physicist (1879–1955)
learned that the German Reichstag had passed the Enabling Act on 23 March, transforming Hitler's government into a de facto legal dictatorship, and that they
Albert_Einstein
State order of Portugal established in 1175
monarchy, the order lost its properties. The ancient military orders were transformed by the liberal constitution and subsequent legislation into mere orders
Military Order of Saint James of the Sword
Military_Order_of_Saint_James_of_the_Sword
Fantasy drama television series
Madoc, a struggling author who imprisons Calliope against her will Derek Jacobi as Erasmus Fry (season 1), a writer of Greek mythology and the original
The_Sandman_(TV_series)
Formal power series
_{i=1}^{r}\prod _{j=1}^{c}{\frac {1}{1-x_{i}y_{j}}}.} Expansions of (formal) Jacobi-type and Stieltjes-type continued fractions (J-fractions and S-fractions
Generating_function
Method of solution for certain mechanical problems
compact. This is usually of practical calculational value when the Hamilton–Jacobi equation is completely separable, and the separation constants can be solved
Action-angle_coordinates
Algorithmic runtime requirements for common math procedures
"An O ( M ( n ) log n ) {\displaystyle O(M(n)\log n)} algorithm for the Jacobi symbol". International Algorithmic Number Theory Symposium. Springer. pp
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Type of differential equation
Continuity equation Heat equation Helmholtz equation Klein–Gordon equation Jacobi equation Lagrange equation Lorenz equation Laplace's equation Maxwell's
Partial_differential_equation
Conjecture in the representation theory of Lie groups
representation (the "Bessel case") or the Weil representation (the "Fourier–Jacobi case"). Let φ = φ 1 × φ 2 {\displaystyle \varphi =\varphi _{1}\times \varphi
Gan–Gross–Prasad_conjecture
Mathematical construct
local zeta-function of a conic section. More generally, such sums for the Jacobi symbol relate to local zeta-functions of elliptic curves and hyperelliptic
Character_sum
Quadratic Gauss sum Gaussian quadrature Gauss–Hermite quadrature Gauss–Jacobi quadrature Gauss–Kronrod quadrature formula Gauss–Newton algorithm Gauss–Legendre
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
a young girl with the ears and tail of a house cat, or the ability to transform from a human into a cat. Male cat people also exist but they are less
List_of_stock_characters
Type of Kac–Moody algebras
these. One may construct generalizations of the Jacobi theta function. These theta functions transform under the modular group. The usual denominator identities
Affine_Lie_algebra
Type of orthogonal polynomials
orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev
Classical orthogonal polynomials
Classical_orthogonal_polynomials
Daughter of Chiron in Greek mythology
Perottus....Cornucopie intitulauit: nuper impressum opera solertissimi viri Jacobi mailleti... (in Latin). impressum per Jacobum Mailleti. p. 289.{{cite book}}:
Hippe
The Weil–Brezin map gives a geometric interpretation of the Fourier transform, the Plancherel theorem and the Poisson summation formula. The image of
Weil–Brezin_Map
Approximation of the definite integral of a function
modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi in 1826. The most common domain of integration for such a rule is taken
Gaussian_quadrature
Welsh actor (born 1969)
starred in the short film Airlock, or How To Say Goodbye in Space with Derek Jacobi and was invited to join the actors' branch of the Academy of Motion Picture
Michael_Sheen
Family of solutions to related differential equations
_{n=1}^{\infty }J_{n}(nz).} Another important relation for integer orders is the Jacobi–Anger expansion: e i z cos ϕ = ∑ n = − ∞ ∞ i n J n ( z ) e i n ϕ {\displaystyle
Bessel_function
Works based on Charles Dickens's 1843 novella
story of Ebenezer Scrooge, a greedy miser who hates Christmas but who is transformed into a caring, kindly person through the visitations of four ghosts (Jacob
Adaptations of A Christmas Carol
Adaptations_of_A_Christmas_Carol
US Supreme Court justice since 2009
Radcliffe Institute, awarded annually to "an individual who has had a transformative impact on society." Sotomayor, Sonia (2022) Just Help! How to Build
Sonia_Sotomayor
JACOBI TRANSFORM
JACOBI TRANSFORM
Boy/Male
Biblical American Hebrew
That supplants, undermines, the heel.
Boy/Male
Spanish
Supplanter.
Female
English
Feminine form of English Jacob, JACOBINA means "supplanter."
Male
Italian
Italian form of Latin Jacobus, JACOPO means "supplanter."
Girl/Female
Australian, Danish, Dutch, French, Hebrew, Latin
Supplants; Female Version of Jacob; Supplanter
Boy/Male
Australian, French, Hebrew, Latin, Spanish
Supplanter; He who Supplants
Male
Spanish
Spanish form of Latin Jacobus, JACOBO means "supplanter."
Boy/Male
Hebrew
Supplanter.
Girl/Female
Australian, Christian, Danish, French, Hebrew, Latin
Supplants; Female Version of Jacob; Supplanter
Female
Dutch
, supplanter.
Male
English
Anglicized form of Greek Iakob and Hebrew Yaaqob, JACOB means "supplanter." In the Old Testament bible, this is the name of a son of Isaac and Rebecca, and the twin brother of Esau. In the New Testament, it is the name of Mary's father-in-law.Â
Boy/Male
Australian, Hebrew
One who Supplants
Male
Dutch
, a Jacobin.
Male
Dutch
, a Jacobin.
Biblical
Yacob, Yacoub - Jacob
Male
English
Variant spelling of English Jacob, JAYCOB means "supplanter."
Female
English
Pet form of English Jackalyn, JACKI means "supplanter."
Male
German
German and Scandinavian form of Greek Iakob, JAKOB means "supplanter."
Female
French
Pet form of French Jacqueline, JACQUI means "supplanter."
Girl/Female
Latin Hebrew Scottish
Supplanter.
JACOBI TRANSFORM
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