In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}...
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the figures at right with domain coloring. The error function at +∞ is exactly 1 (see Gaussian integral). At the real axis, erf z approaches unity at...
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In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician...
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a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this...
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processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would...
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The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...
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_{0}^{a}{\frac {\varphi (hx)}{1+x^{2}}}\,dx} is Owen's T function. Owen has an extensive list of Gaussian-type integrals; only a subset is given below. ∫ φ (...
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Normal distribution (redirect from Gaussian probability density function)
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...
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examples include: Gaussian function, the probability density function of the normal distribution. This is the archetypal bell shaped function and is frequently...
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of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with...
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coordinate axes. Only the Gaussian function is both separable and isotropic. The separable forms of all other window functions have corners that depend...
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function or Dawson integral (named after H. G. Dawson) is the one-sided Fourier–Laplace sine transform of the Gaussian function. The Dawson function is...
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generating function (logarithm of the characteristic function)[contradictory] is the inverse of the cumulant generating function of a Gaussian random variable...
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chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the...
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processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that...
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Wave packet (redirect from Gaussian wave packet)
frequency within a bandwidth inversely proportional to that width; even a gaussian function is considered a wave packet because its Fourier transform is a "packet"...
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List of things named after Carl Friedrich Gauss (redirect from Gaussian)
modified Gaussian distribution or function, used for description of peak shape in many techniques Gauss error function Gaussian process Gaussian filter...
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Ricker wavelet (redirect from Mexican Hat Function)
normalized second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family...
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Copula (statistics) (redirect from Gaussian copula function)
limitations of the Gaussian copula and of copula functions more generally, specifically the lack of dependence dynamics. The Gaussian copula is lacking...
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exponential function – Exponential function of an exponential function Exponential field – Mathematical field with an extra operation Gaussian function Half-exponential...
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distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced sine and cosine transforms...
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_{t}:\mathbb {R} ^{n}\rightarrow \mathbb {R} } denote the radial Gaussian function Φ t ( x ) = N ( x | 0 , t ) {\displaystyle \Phi _{t}(x)={\mathcal...
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In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal...
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definite function. Such functions, including the Gaussian, inverse quadratic, and inverse multiquadric are often used as radial basis functions for this...
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Weierstrass transform (section Gaussian Functions)
{\displaystyle f} , weighted with a Gaussian centered at x {\displaystyle x} . Specifically, it is the function F {\displaystyle F} defined by F ( x...
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Elisabeth; Flyer, Natasha (2011-01-01). "Stable Computations with Gaussian Radial Basis Functions". SIAM Journal on Scientific Computing. 33 (2): 869–892. Bibcode:2011SJSC...
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log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly...
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cosh , {\displaystyle \cosh ,} Gaussian function x ↦ exp ( − x 2 ) . {\displaystyle x\mapsto \exp(-x^{2}).} A real function f is odd if, for every x in...
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{3}})\;X\approx 2.634\;X} where arcsch is the inverse hyperbolic secant. Gaussian function Cutoff frequency Spatial resolution This article incorporates public...
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In physics, a non-Gaussianity is the correction that modifies the expected Gaussian function estimate for the measurement of a physical quantity. In physical...
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