# asymptotic expansion

Also found in: Wikipedia.

## asymptotic expansion

[ā‚sim′täd·ik ik′span·shən]
(mathematics)
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 nN 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.
References in periodicals archive ?
In a very recent study [9], using an asymptotic expansion technique, the asymptotic equations governing unidirectional wave propagation of small-butfinite amplitude long waves in the nonlinear nonlocal elastic medium were derived.
The drawback of this can eliminate by the use of higher order terms [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in asymptotic expansion [24, 25].
Mansour [12] derived an asymptotic expansion of the q-gamma function [[GAMMA].
Using the asymptotic results of Section 2 we derive the following asymptotic expansion
Chinese scholars had proved the following asymptotic expansion of error [2] at the node [x.
First, we recall the principle of the topological asymptotic expansion (Masmoudi, 2001; Amstutz et al.
Following a review of analytic function theory, they discuss special functions, eigenvalue problems and eigenfunction expansions, Green's functions for boundary-value problems, Laplace transform methods, Fourier transform methods, particular physical problems, and asymptotic expansion of integrals.
the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint.
4] Shi Wei, [lambda] globally uniform asymptotic expansion of the hermite polynomials, Acta Mathematica Scientia, 28(2008), 834-842.
This gives a Poincare-type asymptotic expansion, which is usually divergent for fixed values of z.
We do this by finding the leading term in the asymptotic expansion of the correlation kernel using the steepest descent method.
We give asymptotic expansion of certain sums for generalized 2-associated stirling numbers of the second kind, Bernoulli numbers, Euler numbers by Darboux's method.

Site: Follow: Share:
Open / Close