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x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...
the file "erf.dat" contains the values of the erf function and can be produced with the following Matlab commands: t=-2.5:0.01:2.5; E = [ t; erf(t)]; E = E'; save -ascii "erf.dat" E; Own work
The ERF method of finding a particular solution of a non-homogeneous differential equation is applicable if the non-homogeneous equation is or could be transformed to form () = + + +; where , are real or complex numbers and () is homogeneous linear differential equation of any order. Then, the exponential response formula can be applied to each ...
The last expression is the logarithmic mean. = ( >) = (>) (the Gaussian integral) = (>) = (, >) (+) = (>)(+ +) = (>)= (>) (see Integral of a Gaussian function
The function was tabulated by Vera Faddeeva and N. N. Terentyev in 1954. [8] It appears as nameless function w(z) in Abramowitz and Stegun (1964), formula 7.1.3. The name Faddeeva function was apparently introduced by G. P. M. Poppe and C. M. J. Wijers in 1990; [9] [better source needed] previously, it was known as Kramp's function (probably after Christian Kramp).
The distribution is a special case of the folded normal distribution with μ = 0.; It also coincides with a zero-mean normal distribution truncated from below at zero (see truncated normal distribution)
Plot of the Dawson integral function F(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics , the Dawson function or Dawson integral [ 1 ] (named after H. G. Dawson [ 2 ] ) is the one-sided Fourier–Laplace sine transform of the Gaussian function.
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.