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 ?
Olde Daalhuis, Asymptotic expansions of q-gamma, q-exponential and q-bessel functions, Journal of Mathematical Analysis and Applications, 186 (1994), 896-913.
2004), by giving complete asymptotic expansions in terms of the Airy function.
Using the concepts of a neutrix and neutrix limit, the first author gave a general principle for the discarding of unwanted infinite quantities from asymptotic expansions, and this has been exploited particularly in connection with multiplication, convolution and composition of distributions, see [4,5].
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.
The researchers develop solutions to the Korteweg-de Vries and Camassa-Holm equation, asymptotic expansions for the partial sums of the exponential series, and two parameter deformations of Chebyshev polynomials with simple recurrence coefficients.
As a matter of fact, the asymptotic expansions of many special functions are divergent.
In this paper, we first derive asymptotic expansions concerning the preconditioned matrices [P.
In Section 4 we investigate a similar modification applied to uniform asymptotic expansions, and we present the function [K.
In particular, the asymptotic analysis of the above integral is amenable for the saddle-point method to obtain uniform asymptotic expansions for the coefficients in (4) for ([n.

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