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})}...

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...

a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this...

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...

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"...

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...

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...

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...

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}}}...

_{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 (...

coordinate axes. Only the Gaussian function is both separable and isotropic. The separable forms of all other window functions have corners that depend...

modified Gaussian distribution or function, used for description of peak shape in many techniques Gauss error function Gaussian process Gaussian filter...

idea, the gaussian curve starts to concentrate more around the center. By the end, the gaussian function will have become a delta function, representing...

limitations of the Gaussian copula and of copula functions more generally, specifically the lack of dependence dynamics. The Gaussian copula is lacking...

_{t}:\mathbb {R} ^{n}\rightarrow \mathbb {R} } denote the radial Gaussian function Φ t ( x ) = N ( x | 0 , t ) {\displaystyle \Phi _{t}(x)={\mathcal...

examples include: Gaussian function, the probability density function of the normal distribution. This is the archetypal bell shaped function and is frequently...

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...

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...

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...

In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal...

generating function (logarithm of the characteristic function)[contradictory] is the inverse of the cumulant generating function of a Gaussian random variable...

theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly...

{\displaystyle f} , weighted with a Gaussian centered at x {\displaystyle x} . Specifically, it is the function F {\displaystyle F} defined by F ( x...

definite function. Such functions, including the Gaussian, inverse quadratic, and inverse multiquadric are often used as radial basis functions for this...

geodesic editing, guided filtering, and domain transforms. Gaussian filter Gaussian function Gaussian blur Convolution Banterle, F.; Corsini, M.; Cignoni, P...

Elisabeth; Flyer, Natasha (2011-01-01). "Stable Computations with Gaussian Radial Basis Functions". SIAM Journal on Scientific Computing. 33 (2): 869–892. Bibcode:2011SJSC...

reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into...

eigenvalues ±1, ±i. The eigenvectors are "Hermite functions", i.e. Hermite polynomials multiplied by a Gaussian function. See Byron & Fuller (1992) for a description...

distribution given by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution. It is often used in analyzing data from spectroscopy or diffraction...