In mathematics, Gaussian brackets are a special notation invented by Carl Friedrich Gauss to represent the convergents of a simple continued fraction...

In numerical analysis, an n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result...

algorithm Gaussian brackets – described on WolframMathWorld Gaussian's modular arithmetic Gaussian integer, usually written as Z[i] Gaussian prime Gaussian logarithms...

components per matrix element. The Gaussian unitary ensemble GUE ( n ) {\displaystyle {\text{GUE}}(n)} is described by the Gaussian measure with density 1 Z GUE...

In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs...

denominators k1, k2, ... then the relevant recursive relation is that of Gaussian brackets: h n = a n h n − 1 + h n − 2 , k n = a n k n − 1 + k n − 2 . {\displaystyle...

denominators k1, k2, ... then the relevant recursive relation is that of Gaussian brackets: hn = anhn − 1 + hn − 2, kn = ankn − 1 + kn − 2. The successive convergents...

generalizations of Gaussian integrals to the complex plane and to multiple dimensions.: 13–15  Other integrals can be approximated by versions of the Gaussian integral...

indices for more details on notation. Formulae are given in SI units and Gaussian-cgs units. The contravariant electromagnetic four-potential can be defined...

{\displaystyle p_{1}(\Delta x)} s, etc. As the convolution of two Gaussians is just another Gaussian, we have that p m ( Δ x ) = 1 ( 2 π m σ 2 2 ) 1 / 2 exp ⁡...

this system, then one need promote the canonical Dirac brackets, not the canonical Poisson brackets to commutation relations. Examination of the above Hamiltonian...

curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that...

utilized. If the imaging beam has Gaussian distribution, when the truncation ratio (the ratio of the diameter of the Gaussian beam to the diameter of the truncating...

opposite "magnetic charges". Precisely, the total magnetic flux through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field. The...

define the q-binomial coefficients, also known as Gaussian coefficients, Gaussian polynomials, or Gaussian binomial coefficients: ( n k ) q = [ n ] q ! [...

models gives rise to Gaussian statistics. The cold spot may also, as suggested in the references above, be a signal of non-Gaussian primordial fluctuations...

one can move on to define the q-binomial coefficients, also known as the Gaussian binomial coefficients, as [ n k ] q = [ n ] ! q [ n − k ] ! q [ k ] ! q...

the bracket ⟨ , ⟩ {\displaystyle \langle ,\rangle } refers to the inner product on the tangent space induced by the metric tensor and the brackets and...

profiles of the circles of confusion in such a way as to become truly Gaussian. Thereby, it is also deemed to improve the "bokeh" of the lens, that is...

in blob detection. The scale-normalized Laplacian of the Gaussian and difference-of-Gaussian features (Lindeberg 1994, 1998; Lowe 2004) ∇ n o r m 2 L...

determinant as a linear combination of determinants of submatrices, or with Gaussian elimination, which allows computing a row echelon form with the same determinant...

extrapolate to T(0). Gaussian quadrature evaluates the function at the roots of a set of orthogonal polynomials. An n-point Gaussian method is exact for...

their correlation functions; the most notable example is the class of Gaussian processes. Probability distributions defined on a finite number of points...

force η ( t ) {\displaystyle {\boldsymbol {\eta }}\left(t\right)} has a Gaussian probability distribution with correlation function ⟨ η i ( t ) η j ( t...

interpreted as a maximum likelihood method in the context of a (coloured) Gaussian noise model and the associated Whittle likelihood. If the transmitted signal...

through a filter of size larger than ħ (e.g., convolving with a phase-space Gaussian, a Weierstrass transform, to yield the Husimi representation, below), results...

independent identically distributed Gaussian noise, then the columns of T will also contain similarly identically distributed Gaussian noise (such a distribution...

{\displaystyle {n \choose k}} is the binomial coefficient. Thus, e.g., Gaussians compose hyperbolically, exp ⁡ ( − a ( q 2 + p 2 ) )   ⋆   exp ⁡ ( − b...

under constraints of mean and variance is the Gaussian.: 255  Let g ( x ) {\displaystyle g(x)} be a Gaussian PDF with mean μ and variance σ 2 {\displaystyle...

connection (or covariant differentiation) ∇ {\displaystyle \nabla } and Lie bracket [ ⋅ , ⋅ ] {\displaystyle [\cdot ,\cdot ]} by the following formula: R (...