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...

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 image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician...

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

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}}}...

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

_{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 (...

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

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

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...

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 theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that...

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

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

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...

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

chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the...

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

expected value x0; it is invariant under translations. If the FWHM of a Gaussian function is known, then it can be integrated by simple multiplication. In spectroscopy...

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

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

uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as...

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...

exponential function – Exponential function of an exponential function Exponential field – Mathematical field with an extra operation Gaussian function Half-exponential...

sample of the training set. Gaussian function Kernel (statistics) Polynomial kernel Radial basis function Radial basis function network Obst kernel network...

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...

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

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