asymptotic expansion

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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 ?
They cover asymptotic expansions and series, asymptotic methods for solving nonlinear equations, the perturbation of nonlinear oscillations, a nonlinear oscillator in a potential well, auto-resonances in nonlinear systems, asymptotics for loss of stability, and systems of coupled oscillators.
In particular, we will study existence, multiplicity and asymptotic expansions of solutions when the competition parameter tends to infinity.
epsilon],[delta]](*) by constructing asymptotic expansions of its probability densities, which are associated with the adjoint operator [L.
by allowing further terms in the asymptotic expansions with exponents between [alpha] and [alpha] + 1, with additional assumptions on the coefficients.
Using asymptotic expansions, Efron (1975) demonstrated that LLD can be less efficient than LDA when the assumptions of LDA are satisfied.
Olde Daalhuis, Asymptotic expansions of q-gamma, q-exponential and q-bessel functions, Journal of Mathematical Analysis and Applications, 186 (1994), 896-913.
The main purpose of this paper is to obtain the first term in the asymptotic expansions of [[phi].
Asymptotic expansions and analytic continuations of the H-function have been discussed by Braaksma ((1)).
In the context of computing asymptotic expansions of sums and series, usually the most useful form of the Euler-Maclaurin formula is
4), we use the ideas from [6,10] of asymptotic expansions of the Bessel functions.

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