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Asymptotic Expansions
| Content Provider | Scilit |
|---|---|
| Author | Zwillinger, Daniel |
| Copyright Year | 1992 |
| Description | Under appropriate smoothness and boundedness conditions, the integral!(..\) = I: h(..\t)j(t) dt bas the asymptotic expansion gral!(..\) = I: ei~t f(t) dt (which is a special case of Special Case 1), has the asymptotic expansion gral!(..\) = I: e-~t f(t) dt (which is a special case of Special Case 1), bas the asymptotic expansion Watson's Lemma (Bleistein and Handelsman [2], page 103, or Wong [5], page 20): If /(t) is locally absolutely integrable on (O,oo), as t-+ oo, /(t) = O(e0 ') for some real number a, and, as t -+ 0+, /(t) "' E:=0 c,.t•m, where Re(am) 43. Asymptotic Expansions Theorem (Bleistein and Handelsman [2], page 120): Let h(t) and /(t) be sufficiently smooth functions on the infinite interval {0, oo) having the asymptotic forms with some conditions on the range of the parameters appearing in the expansion. Let the Mellin transforms of h and I be denoted by M[h; z] and M[/; z] (see the Notes). If some technical conditions are satisfied, then represents a finite asymptotic expansion as ~ -+ oo with respect to the asymptotic sequence p-oi(log~)nrm}. The expression in {43.2) represents a sum of the residues over all of the poles in a specific region of the complex plane. Book Name: The Handbook of Integration |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2010-0-47201-8&isbn=9780429108372&doi=10.1201/9781439865842-51&format=pdf |
| Ending Page | 214 |
| Page Count | 4 |
| Starting Page | 211 |
| DOI | 10.1201/9781439865842-51 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 1992-11-02 |
| Access Restriction | Open |
| Subject Keyword | Book Name: The Handbook of Integration Mathematical Physics Functions Asymptotic Expansion Expansion Gral |
| Content Type | Text |
| Resource Type | Chapter |
