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Formula for the Legendre polynomials
Rodrigues' formula (formerly called the Ivory–Jacobi formula) generates the Legendre polynomials. It was independently introduced by Olinde Rodrigues (1816)
Rodrigues'_formula
Vector formula for a rotation in space, given its axis
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector
Rodrigues'_rotation_formula
Formula for 3D vector rotation
mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula, but uses a different
Euler–Rodrigues_formula
French banker and mathematician (1795–1851)
mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula for the Legendre polynomials, and the Euler–Rodrigues parameters
Olinde_Rodrigues
System of complete and orthogonal polynomials
especially compact expression for the Legendre polynomials is given by Rodrigues' formula: P n ( x ) = 1 2 n n ! d n d x n ( x 2 − 1 ) n . {\displaystyle P_{n}(x)={\frac
Legendre_polynomials
Polynomial sequence
\lfloor n/2\rfloor }(\rho ^{2}).} The radial polynomials satisfy the Rodrigues' formula R n m ( x ) = 1 ( n − m 2 ) ! x m ( d d ( x 2 ) ) n − m 2 [ x n +
Zernike_polynomials
Type of orthogonal polynomials
{R} } . The Wikipedia article Rodrigues' formula has a proof that the polynomials obtained from the Rodrigues' formula obey a differential equation of
Classical orthogonal polynomials
Classical_orthogonal_polynomials
Polynomial sequence
+m+1)}}\left({\frac {z-1}{2}}\right)^{m}.} An equivalent definition is given by Rodrigues' formula: P n ( α , β ) ( z ) = ( − 1 ) n 2 n n ! ( 1 − z ) − α ( 1 + z ) −
Jacobi_polynomials
Special orthogonal group
rotation Four-dimensional rotations can be derived from Rodrigues' rotation formula and the Cayley formula. Let A be a 4 × 4 skew-symmetric matrix. The skew-symmetric
Rotations in 4-dimensional Euclidean space
Rotations_in_4-dimensional_Euclidean_space
-1)P_{n-1}(x;\phi ).} The Meixner–Pollaczek polynomials are given by the Rodrigues-like formula P n ( λ ) ( x ; ϕ ) = ( − 1 ) n n ! w ( x ; λ , ϕ ) d n d x n w
Meixner–Pollaczek_polynomials
Sequence of differential equation solutions
L0, L1, ..., are a polynomial sequence which may be defined by the Rodrigues formula, L n ( x ) = e x n ! d n d x n ( e − x x n ) = 1 n ! ( d d x − 1 )
Laguerre_polynomials
Family of orthogonal polynomials
} The continuous Hahn polynomials are given by the Rodrigues-type formula Γ ( a + i x ) Γ ( b + i x ) Γ ( c − i x ) Γ ( d − i x ) p n ( x
Hahn_polynomials
Mathematics concept
-1)(n+\alpha -2k)_{k-1}} and n ≥ 0 {\displaystyle n\geq 0} . The Rodrigues formula for the Bessel polynomials as particular solutions of the above differential
Bessel_polynomials
zeta function. Euler–Maclaurin formula (Euler's summation formula) relating integrals to sums Euler–Rodrigues formula describing the rotation of a vector
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Matrix representing a Euclidean rotation
This is a matrix form of Rodrigues' rotation formula, (or the equivalent, differently parametrized Euler–Rodrigues formula) with u ⊗ u = u u T = [ u
Rotation_matrix
Ways to represent 3D rotations
to demonstrate these facts. The Rodrigues vector (sometimes called the Gibbs vector, with coordinates called Rodrigues parameters) can be expressed in
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Set of polynomials where any two are orthogonal to each other
Legendre polynomials as special cases. These are frequently given by the Rodrigues' formula. The field of orthogonal polynomials developed in the late 19th century
Orthogonal_polynomials
Topics referred to by the same term
Rodrigues is an island in the Indian Ocean, administratively part of Mauritius. Rodrigues may also refer to: Rodrigues triple junction, a tectonic triple
Rodrigues_(disambiguation)
Polynomial sequence
{d^{n}}{dx^{n}}}e^{-x^{2}}.} These equations have the form of a Rodrigues' formula and can also be written as, He n ( x ) = ( x − d d x ) n ⋅ 1 , H
Hermite_polynomials
Four-dimensional number system
Johan E. (2007). "Derivation of the Euler–Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations". arXiv:math/0701759
Quaternion
Canonical solutions of the general Legendre equation
{d}{dx}}P_{\ell }(x)+\ell (\ell +1)P_{\ell }(x)=0.} Moreover, since by Rodrigues' formula, P ℓ ( x ) = 1 2 ℓ ℓ ! d ℓ d x ℓ [ ( x 2 − 1 ) ℓ ] , {\displaystyle
Associated Legendre polynomials
Associated_Legendre_polynomials
Parameterization of a rotation into a unit vector and angle
to locate it in any particular Cartesian coordinate frame. By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional
Axis–angle_representation
Shape designed to roll down some path
existence of trajectoids follows from Minkowski's theorem and the Rodrigues formula for the product of rotation matrices. Sobolev, Yaroslav I.; Dong,
Trajectoid
Form of a matrix
the matrix exponential is Rodrigues' rotation formula in matrix notation, and when expressed via the Euler-Rodrigues formula, the algebra of its four parameters
Skew-symmetric_matrix
Mathematics concept
Cauchy polynomials in their applications in random matrix theory. The Rodrigues formula specifies the polynomial R(α,β) n(x) as where Nn is a normalization
Romanovski_polynomials
Polynomial sequence
factorial of θ {\displaystyle \theta } . One therefore also has the Rodrigues formula C n ( α ) ( x ) = ( − 1 ) n 2 n n ! Γ ( α + 1 2 ) Γ ( n + 2 α ) Γ
Gegenbauer_polynomials
Correspondence between quaternions and 3D rotations
This is Rodrigues' rotation formula for the axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Four integers where the sum of the squares of three equals the square of the fourth
Beal conjecture Euler brick Euler's sum of powers conjecture Euler-Rodrigues formula for 3D rotations Fermat cubic Jacobi–Madden equation Lagrange's four-square
Pythagorean_quadruple
Macanese racing driver (born 2007)
Championship. Rodrigues participated in the X30 Senior Macanese Championship at Coloane Karting Track [zh] for the first time in 2022. Rodrigues would finish
Tiago Rodrigues (racing driver)
Tiago_Rodrigues_(racing_driver)
Mathematical method in calculus
the integrand, and proves useful, too (see Rodrigues' formula). The essential process of the above formula can be summarized in a table; the resulting
Integration_by_parts
Mathematical functions
) {\displaystyle g_{n}(x)} satisfy a Rodrigues' formula involving the central difference operator. This formula can be derived using their connection
Mittag-Leffler_polynomials
Movement with a fixed point is rotation
see screw axis. This gives rise to screw theory. Euler angles Euler–Rodrigues formula Rotation formalisms in three dimensions Angular velocity Rotation
Euler's_rotation_theorem
Q-analog of the ordinary derivative
are used to q {\displaystyle q} -Taylor formula and the q {\displaystyle q} -Rodrigues' formula (the formula used to construct q {\displaystyle q} -orthogonal
Q-derivative
Eight-dimensional algebra over the real numbers
{\hat {\alpha }}{2}}{\mathsf {B}}\cdot {\mathsf {A}}}}.} This is Rodrigues' formula for the screw axis of a composite displacement defined in terms of
Dual_quaternion
Elementary particles with a spin of 1/2
\alpha } about a unit direction m {\displaystyle {\boldsymbol {m}}} , Rodrigues' formula says R m ( n ) = n cos α + ( m × n ) sin α + m ( m ⋅ n ) ( 1 −
Spin_1/2
Bernhard Riemann: Riemann zeta function, Riemann xi function Olinde Rodrigues: Rodrigues formula Leonard James Rogers: Rogers–Askey–Ismail polynomial, Rogers–Ramanujan
List of eponyms of special functions
List_of_eponyms_of_special_functions
Type of matrix
the matrix exponential is Rodrigues' rotation formula in matrix notation, and when expressed via the Euler-Rodrigues formula, the algebra of its four parameters
Infinitesimal_rotation_matrix
Group of rotations in 3 dimensions
as a matrix for a rotation around axis u by the angle θ: cf. Rodrigues' rotation formula. Given R ∈ SO(3), let A = 1 2 ( R − R T ) {\displaystyle A={\tfrac
3D_rotation_group
Class of mathematical polynomials
In mathematics, Racah polynomials are orthogonal polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality
Racah_polynomials
Spinor topology
fixed) as its vector part (also called imaginary part, see Euler–Rodrigues formula). If the initial orientation of a rigid body (with unentangled connections
Orientation_entanglement
Motorsport season
BlackJack Racing to Team Up in 2023 Formula 4 South East Asia". Asia Racing Team. 2023-08-14. "Macau's Tiago Rodrigues Gears Up for Hometown Grand Prix"
2023 Formula 4 South East Asia Championship
2023_Formula_4_South_East_Asia_Championship
Scottish mathematician (1765–1842)
Eclipse Meridian arc Probability Proofs of Fermat's little theorem Rodrigues' formula O'Connor, John J.; Robertson, Edmund F., "James Ivory", MacTutor History
James_Ivory_(mathematician)
Jonsson Formula 4 CEZ Championship Ethan Ischer 2023 Formula 4 CEZ Championship Teams: Jenzer Motorsport F4 Chinese Championship Tiago Rodrigues 2023 F4
List of 2023 motorsport champions
List_of_2023_motorsport_champions
Annual motorsport event
unimpressed by controversial Macau GP Formula Regional switch". Autosport. "Grande Prémio: Tiago Rodrigues diz que Fórmula Regional vai atrair mais pilotos
Macau_Grand_Prix
Novel by José Rodrigues dos Santos
Fórmula de Deus (God's Formula), in English The Einstein Enigma, is the fourth novel written by the Portuguese journalist and writer José Rodrigues dos
A_Fórmula_de_Deus
colleagues. Rodrigues has three children: Jacqueline, João Paulo and Renato, from her marriage with Renato Martins [pt], who is also Formula Truck driver
Débora_Rodrigues
Motorsport team from Australia
and has since competed in the Formula Regional Asian Championship and the GB4 Championship. It will enter the Formula Regional Middle East Championship
Evans_GP
Brazilian drag queen and singer (born 1993)
Phabullo Rodrigues da Silva (born 1 November 1993), known professionally as Pabllo Vittar (Portuguese pronunciation: [ˈpablu viˈtaʁ]), is a Brazilian
Pabllo_Vittar
Portuguese journalist and novelist
José António Afonso Rodrigues dos Santos (born 1 April 1964) is a Portuguese journalist, novelist and university lecturer. He has been one of the presenters
José_Rodrigues_dos_Santos
Formula 4 championship season
(Trophy) Parent series: Formula Regional Middle East Championship The 2024 Formula 4 UAE Championship was the eighth season of the Formula 4 UAE Championship
2024 Formula 4 UAE Championship
2024_Formula_4_UAE_Championship
Brazilian politician
Party (PT). From 1997 to 2005, Rodrigues served as mayor of Belém. As a Federal Deputy, first elected in 2015, Rodrigues did not support the impeachment
Edmilson_Rodrigues
Brazilian racing driver (1960–1994)
two of Formula One's most famous names". The Daily Telegraph. London. Archived from the original on 12 May 2014. Retrieved 11 March 2015. Rodrigues, Ernesto
Ayrton_Senna
First edition of the FIA F4 World Cup
2025年國際汽聯四級方程式世界盃), officially the 2025 Macau Formula 4 Race – FIA F4 World Cup, was a motor race for Formula 4 (F4) cars held on the Guia Circuit, a street
2025_FIA_F4_World_Cup
Brazilian racing driver (born 1952)
racing driver and businessman, who competed in Formula One from 1978 to 1991. Piquet won three Formula One World Drivers' Championship titles, which he
Nelson_Piquet
Racecar innovation
February 20, 2020. Rodrigues, Cadmo; Landre Junior, Janes (March 2022). "Review of the dual-axis steering system used by Mercedes-AMG in Formula One". 2021 SAE
Dual-axis_steering
Formula 4 championship season
F4 rookie cup winner Martin Molnar returns with Virtuosi". Formula Scout. "Tiago Rodrigues Rejoins Evans GP for 2025 F4 Middle East Championship". Evans
2025 F4 Middle East Championship
2025_F4_Middle_East_Championship
71st running of the Macau Grand Prix
held as a domestic Formula 4 event for three years, serving as a round of the Chinese Formula 4 Championship. After a return of Formula 3 and other international
2024_Macau_Grand_Prix
2024 Brazilian television miniseries on Ayrton Senna
in Formula Ford James Marlowe as Ralph Firman Sr., Senna's team boss in Formula Ford Charlie Hamblett as Martin Brundle, Senna's rival in Formula Three
Senna_(miniseries)
Women's motor racing championship held in 2025
Bull and Ford backing for 2025 F1 Academy drive". Formula Scout. Retrieved 8 October 2024. Rodrigues, Bruna; Peçanha, Breno (30 October 2024). "Rafaela
2025_F1_Academy_season
Country in North America
legislative ties to Britain, as well as adding a constitutional amending formula and the Canadian Charter of Rights and Freedoms. The Charter guarantees
Canada
Hall Kart Racing School". Na-motorsports.com. Retrieved July 20, 2009. "Formula 1 and Indy Car Racing Blog: Women at Sebring". No Fenders. March 13, 2008
List of family relations in auto racing
List_of_family_relations_in_auto_racing
Motorsport event
The 2023 Macau Formula 4 Race, also called the 2023 Macau Asia Formula 4, was a Formula 4 (F4) motor race held on the Guia Circuit in Macau on 12 November
2023_Macau_Formula_4_Race
Canadian actor (born 1964)
Archived from the original on January 14, 2024. Retrieved January 14, 2024. Rodrigues, Leonardo (August 31, 2019). "Conquest: Tudo o que sabemos sobre a série
Keanu_Reeves
Car racing series
according to FIA Formula 4. The inaugural season was the 2015–16 edition. Gerhard Berger and the FIA Singleseater Commission launched the FIA Formula 4 in March
F4_Chinese_Championship
Chinese auto racing team
2016. Having also raced in the TCR Asia Series, Asian Formula Renault Series and China Formula 4 Championship amongst others. Having first entered the
Champ_Motorsport
Motorsport season
2024 Formula 4 Australian Championship Drivers' Champion: James Piszcyk Rookies' Champion: Seth Gilmore Masters' Champion: Nathan Gotch Previous 2019
2024 Formula 4 Australian Championship
2024_Formula_4_Australian_Championship
Family of mammals
hdl:10261/388427. ISSN 0272-4634. Rodrigues-Oliveira, Igor Henrique; Batista da Silva, Iuri; Rocha, Renan Rodrigues; Soares, Rafael Augusto Silva; Menegidio
Felidae
Indoor arena in London, England
21 June 2007. Retrieved 25 May 2010. Halliday, Josh; Morris, Steven; Rodrigues, Jason; Greenfield, Patrick (18 February 2022). "Storm Eunice live: winds
The_O2_Arena
Heads of government of Indian states
1897 Governor Joaquim José Machado 1897 1900 Governor Eduardo Augusto Rodrigues Galhardo 1900 1905 Government Council of the State of India D. António
List of office-holders in India
List_of_office-holders_in_India
French mathematician (1906-1998)
List Bergman–Weil formula Borel–Weil theorem Chern–Weil homomorphism Chern–Weil theory De Rham–Weil theorem Weil's explicit formula Hasse–Weil Bound Hasse–Weil
André_Weil
Dominican diplomat and playboy (1909–1965)
Crawford, Veronica Lake, Kim Novak, Judy Garland, Eva Perón and Amália Rodrigues. He dallied with his ex-wife Flor de Oro Trujillo Ledesma during his marriage
Porfirio_Rubirosa
Pejorative for musical artists
ready to be very, very famous". The Fader. Retrieved 29 December 2023. Rodrigues, Ashwin (29 October 2020). "Jean Dawson Made a Record for His 17-Year-Old
Industry_plant
Country in Southwestern Europe
(2021), pp. 91–105. Aires Oliveira (2017). Júnior (2021), pp. 121–137. Rodrigues (2021), pp. 107–128. Pimentel (2024), pp. 121–146. Andrade (2024), pp
Portugal
English association football league
Archived from the original on 17 March 2022. Retrieved 20 December 2018. Rodrigues, Jason (2 February 2012). "Premier League football at 20: 1992, the start
Premier_League
Capital and largest city of Pará, Brazil
turistic website here. Inspired by the Bois de Boulogne Park in Paris, the Rodrigues Alves Wood is an environmental preservation area in the middle of the
Belém
Endurance racing team
German Formula 3 before moving to the F3 Euro Series from 2003 to 2005. Colin Kolles left the team to become director of the Jordan Grand Prix Formula One
ByKolles_Racing
English actor (born 1964)
Hiddleston and Jeremy Irons. Later in 2014, Purefoy co-starred in the Formula 1-themed music video for David Guetta's song "Dangerous". From 2016 to
James_Purefoy
Sailing regatta
49er FX, mixed Nacra 17, men's and women's IQFoil, and men's and women's Formula Kite. In 2014, the Semaine Olympique Française in Hyères became an event
Semaine_Olympique_Française
Maximum weight that can be lifted at once
w} is a factor of each formula, so the unit of measurement doesn't matter). Of the formulas, the Epley and the Brzycki formulas are most commonly used
One-repetition_maximum
110022. McGrath, K.; van der Sluis, L. G.; Lefebvre, A.; Charpentier, A.; Rodrigues, A. S. L.; Álvarez-Fernández, E.; et al. (2025). "Late Paleolithic whale
2025_in_paleomammalogy
nanoen.2014.12.021. Kumar, B.; Kumar, J.; Leese, R.; Fellner, J. P.; Rodrigues, S. J.; Abraham, K. M. (2010). "A Solid-State, Rechargeable, Long Cycle
Research in lithium-ion batteries
Research_in_lithium-ion_batteries
conducting clinical trials and field tests. They derived its chemical formula and determined how it works. The private sector and the United States Department
Discovery_of_penicillin
- Olga Cardoso) Agarra a Música (2017 - Cláudia Vieira and João Paulo Rodrigues) Agora É que Conta (2010–2011) Apanha se Puderes (Portuguese version of
List of international game shows
List_of_international_game_shows
Edition of motorsport championship
for the first time. The season was overshadowed by the death of Hoosier Formula Cup gentleman driver Walter Rykart, who passed away between the first and
2026 Ultimate Cup European Series
2026_Ultimate_Cup_European_Series
Process of repeating items in a self-similar way
claims about the Pirahã language. Andrew Nevins, David Pesetsky and Cilene Rodrigues are among many who have argued against this. Literary self-reference can
Recursion
Oregon Bach Festival, Internationale Bachakademie Stuttgart). Tânia Rodrigues, 75, Brazilian politician, Rio de Janeiro MLA (1995–2003, 2015–2019).
Deaths_in_February_2026
Sports season
The 2004 Championnat de France Formula Renault 2.0 was a highly competitive racing series held in France. Patrick Pilet emerged as the champion, showcasing
2004 Championnat de France Formula Renault 2.0
2004_Championnat_de_France_Formula_Renault_2.0
Species of carnivore
Company. pp. 192–206. ISBN 978-0-442-22430-1. OL 5059407M. Rodden, M.; Rodrigues, F.; Bestelmeyer, S. (2004). "Chapter 3. South America (Neotropical)"
Maned_wolf
Chemical compound
Squalane is the organic compound with the formula ((CH3)2CH[CH2]3CH(CH3)[CH2]3CH(CH3)[CH2]2)2. A colorless hydrocarbon, it is the hydrogenated derivative
Squalane
1973 television film by John L. Moxey
animation. The film stars Alex Cord, Mariette Hartley, Ted Cassidy, Percy Rodrigues, Harvey Jason, Titos Vandis, Bill Striglos, Lynne Marta, Harry Raybould
Genesis_II_(film)
1914 executions and looting in Belgium
from your work. To conclude this letter, I search in vain for the polite formula appropriate to the nature of our relationship. Please allow me, Professor
Sack_of_Dinant
Association football club in England
Archived from the original on 10 January 2022. Retrieved 30 June 2018. Rodrigues, Jason (2 February 2012). "Premier League football at 20: 1992, the start
Tottenham_Hotspur_F.C.
2023 Indian film by Siddharth Anand
red-carpet entry for Shah Rukh Khan into the YRF Spy Universe with its right formula of high-octane death and logic-defying action sequences seasoned with desh
Pathaan_(film)
French racing driver
in La Roche-sur-Yon) is a French former racing driver. Marroc began his formula racing career in the 2006 Championnat de France FFSA Formule Campus Renault
Nicolas_Marroc
and coach David Rodman (born 1983), Slovenian ice hockey player David Rodrigues (born 1991), Portuguese cyclist David Roe (born 1965), English snooker
List of people with given name David
List_of_people_with_given_name_David
Lack of or little sexual attraction to others
1080/00224499.2019.1689378. ISSN 0022-4499. PMID 31799860. Carvalho, A. Catarina; Rodrigues, David L. (March 1, 2025). "Belonging to the Ace Spectrum: Correlates
Asexuality
Synchetic chemical compound
69S. doi:10.2138/gselements.17.1.69. Tomás, Helena; Alves, Carla S.; Rodrigues, João (2018). "Laponite®: A key nanoplatform for biomedical applications
Laponite
Name list
born 1998) (Emerson Barbosa Rodrigues dos Santos), Brazilian footballer Emerson (footballer, born 2002) (Emerson Rodrigues Brito), Brazilian footballer
Emerson_(given_name)
Roundup and similar herbicides
PMC 6040695. PMID 29995880. Rodrigues NR, de Souza AP (April 2018). "Occurrence of glyphosate and AMPA residues in soy-based infant formula sold in Brazil". Food
Glyphosate-based_herbicides
Name list
political theorist Bruno Rodrigo (born 1985), Brazilian footballer Bruno Rodrigues, multiple people Bruno Rodríguez, multiple people Bruno Rodzik (1935–1998)
Bruno_(name)
travel, tourism, insurance
RODRIGUES FORMULA
RODRIGUES FORMULA
RODRIGUES FORMULA
RODRIGUES FORMULA
RODRIGUES FORMULA
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RODRIGUES FORMULA
RODRIGUES FORMULA
RODRIGUES FORMULA
travel, tourism, insurance