Taylor's Theorem
Taylor's Theorem :
(1) If all the derivatives of a function fix) are continuous in the vicinity of x = a, then/fa) can be expressed in an infinite series (the Taylor series): fix) = fid) +f\x) (x-a) + ±f'{x) (x -a)1+ ...+ -l/w(a)(x-a)" + ... n\. The case a=0 is called a Maclaurin series. (2) The theorem of G.I. Taylor in the statistical theory of atmospheric turbulence: where x is the distance traveled by a particle in the time interval T, u is the fluctuation or eddy velocity of the particle, and /?(£) is the Lagrangian correlation coefficient between the particle's velocity at time t and / + N.B. Refer to source to verify equation(s)
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