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The Gauss gun (often called a Gauss rifle or Gauss cannon) is a device that uses permanent magnets and the physics of the Newton's cradle to accelerate a projectile. Gauss guns are distinct from and predate coil guns , although many works of science fiction (and occasionally educators [ 1 ] ) have confused the two.
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
Plot of the hypergeometric function 2F1(a,b; c; z) with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics , the Gaussian or ordinary hypergeometric function 2 F 1 ( a , b ; c ; z ) is a special function represented by the hypergeometric series , that ...
Although the "GR" designation purports the device to be a "Gauss Rifle", as evidenced both by the company [1] and media reports, [2] [3] this is technically a misnomer on two counts—it is neither a rifle (as it doesn't use rifling) nor a Gauss gun (a type of accelerator that uses permanent magnets and is distinct from a coilgun).
Ideal line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. [1] Actual line shapes are determined principally by Doppler, collision and proximity broadening. For each system the half-width of the shape function varies with temperature, pressure (or concentration) and
where is the amplitude of Gaussian, = is exponent relaxation time, is a variance of exponential probability density function. This function cannot be calculated for some values of parameters (for example, =) because of arithmetic overflow.
Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials.
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.