Taylor Theorem

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Taylor Theorem

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1. If all the derivatives of a function f(x) are continuous in the vicinity of x = a , then f(x) can be expressed in an infinite series (the Taylor series):

Missing Image:img src="SP7_t_files/taylor1.gif"

The case a = 0 is called a Maclaurin series. </dd>
2. The theorem of G.I. Taylor in the statistical theory of atmospheric turbulence:

Missing Image:img src="SP7_t_files/taylor2.gif"

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 R(ξ) is the Lagrangian correlation coefficient between the particle's velocity at time t and t + ξ. </dd>

References

This article is based on NASA's Dictionary of Technical Terms for Aerospace Use