Group theory, some simple results from category theory, Shannon theory completely missing.Ĭomplete lack of various numbering systems ( binary, hex at least) Congruences nearly omitted ( Chinese remainder theorem maybe) No various number theory objects: Mobius function, Minkowski function ?() not mentioned. No elliptic functions, no Weierstrass function mentioned. Special functions: Bessel, Jacobi, Lagrange, Chevyshev polynomials, various equations related to it. Hydrodynamic, notable no Navier-Stokes equations. Quantum physics, Heisenberg relation at least please! Notable: Laplace equation and Maxwell-Clerk equations, wave equation!!! However the choice of various areas is strange for me ( partially lack of some engineering areas, partially lack of very basic physics things, partially lack of mathematics)Ī lot of things is missing: Maxwell-Clerk equations. I have a loose suggestion - it could be published together with LaTeX codes for any formula present - so it would be great speed up for someone who wants to use various formula in his works. The characteristic function was a Fourier transform of a PDF, so an inverse Fourier transform gets it back:īut the Fourier transform of a Gaussian is just a Gaussian. These terms from expanding the log of the characteristic function constitute the cumulant expansion and for large n the other terms shrink to zero, so that the characteristic function is to first order in 1/n a Gaussian. If two variables X ~ r and Y ~ s are independent then you can prove that their sum has a characteristic functionĪnd therefore the “sample mean” M of n IID variables is itself a random variable with characteristic function The easiest is to look at characteristic functions and cumulants for a random variable T with PDF p(t) we say T ~ p and define
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December 2022
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