Rodrigues' formula (formerly called the Ivory–Jacobi formula) generates the Legendre polynomials. It was independently introduced by Olinde Rodrigues (1816)...

In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector...

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...

mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula for the Legendre polynomials, and the Euler–Rodrigues parameters...

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...

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...

π] noted previously (Miles 1965). Euler–Rodrigues formula Euler's rotation theorem Rodrigues' rotation formula Plane of rotation Axis–angle representation...

interferometers and the open source software DFTFringe. They satisfy the Rodrigues' formula Z n m ( x ) = x − m ( n − m 2 ) ! ( d d ( x 2 ) ) n − m 2 [ x n +...

+m+1)}}\left({\frac {z-1}{2}}\right)^{m}.} An equivalent definition is given by Rodrigues' formula:: IV.3  P n ( α , β ) ( z ) = ( − 1 ) n 2 n n ! ( 1 − z ) − α ( 1...

{R} } . The Wikipedia article Rodrigues' formula has a proof that the polynomials obtained from the Rodrigues' formula obey a differential equation of...

to demonstrate these facts. The Rodrigues vector (sometimes called the Gibbs vector, with coordinates called Rodrigues parameters) can be expressed in...

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 )...

{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...

zeta function. Euler–Maclaurin formula (Euler's summation formula) relating integrals to sums Euler–Rodrigues formula describing the rotation of a vector...

-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...

-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...

Rodrigues is an island in the Indian Ocean, administratively part of Mauritius. Rodrigues may also refer to: Rodrigues triple junction, a tectonic triple...

Legendre polynomials as special cases. These are frequently given by the Rodrigues' formula. The field of orthogonal polynomials developed in the late 19th century...

} This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840 (see...

to locate it in any particular Cartesian coordinate frame. By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional...

the integrand, and proves useful, too (see Rodrigues' formula). The essential process of the above formula can be summarized in a table; the resulting...

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...

see screw axis. This gives rise to screw theory. Euler angles Euler–Rodrigues formula Rotation formalisms in three dimensions Angular velocity Rotation...

} This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840 (see...

\end{aligned}}} The continuous Hahn polynomials are given by the Rodrigues-like formula Γ ( a + i x ) Γ ( b + i x ) Γ ( c − i x ) Γ ( d − i x ) p n ( x...

{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...

Johan E. (2007). "Derivation of the Euler–Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations". arXiv:math/0701759...

the matrix exponential is Rodrigues' rotation formula in matrix notation, and when expressed via the Euler-Rodrigues formula, the algebra of its four parameters...

fixed) as its vector part (also called imaginary part, see Euler–Rodrigues formula). If the initial orientation of a rigid body (with unentangled connections...

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...