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Faddeeva Function
The Faddeeva function or Kramp function is a scaled complex complementary error function, :w(z):=e^\operatorname(-iz) = \operatorname(-iz) =e^\left(1+\frac\int_0^z e^\textt\right). It is related to the Fresnel integral, to Dawson's integral, and to the Voigt function. The function arises in various physical problems, typically relating to electromagnetic responses in complicated media. * problems involving small-amplitude waves propagating through Maxwellian plasmas, and in particular appears in the plasma's permittivity from which dispersion relations are derived, hence it is sometimes referred to as the plasma dispersion function (although this name is sometimes used instead for the rescaled function defined by ''Fried and Conte'', 1961). * the infrared permittivity functions of amorphous oxides have resonances (due to phonons) that are sometimes too complicated to fit using simple harmonic oscillators. The Brendel–Bormann oscillator model uses an infinite superposition o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faddeeva
In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non- elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of , the error function has the following interpretation: for a random variable that is normally distributed with mean 0 and standard deviation , is the probability that falls in the range . Two closely related functions are the complementary error function () defined as :\operatorname z = 1 - \operatorname z, and the imaginary error function () defined as :\operatorname z = -i\operatorname iz, where is the imaginary unit Name The name "error function" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
