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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 ...
When the non-homogeneous term is expressed as an exponential function, the ERF method or the undetermined coefficients method can be used to find a particular solution. If non-homogeneous terms can not be transformed to complex exponential function, then the Lagrange method of variation of parameters can be used to find solutions.
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.
The last expression is the logarithmic mean. = ( >) = (>) (the Gaussian integral) = (>) = (, >) (+) = (>)(+ +) = (>)= (>) (see Integral of a Gaussian function
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)
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).
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.
For example, in the checkerboard paradigm described above, healthy participants' first response of the visual cortex is around 50–70 ms. This would seem to indicate that this is the amount of time it takes for the transduced visual stimulus to reach the cortex after light first enters the eye .