asymptotic expansion(redirected from Asymptotic scale)
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asymptotic expansion[ā‚sim′täd·ik ik′span·shən]
A series of the form a0+ (a1/ x) + (a2/ x 2) + · · · + (an / xn) + · · · is an asymptotic expansion of the function f (x) if there exists a number N such that for all n ≠ N the quantity xn [f (x) -Sn (x)] approaches zero as x approaches infinity, where Sn (x) is the sum of the first n terms in the series. Also known as asymptotic series.