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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).
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Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
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.
It becomes clear that the optimization the log-likelihood with respect to the two parameters has turned into a root search of a function. This of course is identical to the previous root search. Tsagris et al. (2014) spotted that there are three roots to this equation for μ {\displaystyle \mu } , i.e. there are three possible values of μ ...