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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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01 Jan 1964
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as discussed by the authors, while a published version is the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication

6 citations

Journal ArticleDOI
TL;DR: In this article, uniform asymptotic approximations for solutions of Mathieu's equation were derived by an application of a theory of a coalescing turning point and simple pole in the complex plane.
Abstract: Uniform asymptotic approximations are derived for solutions of Mathieu's equation —Y = {2qcos(2z) ajw, for a and q real, and z complex. These are uniformly valid for q large and a lying in the interval —2q < a < (2 — d)q, (d > 0), for all real or complex values of z. The approximations involve both elementary functions (LiouvilleGreen) and Whittaker functions. These results are derived by an application of a recent asymptotic theory of a coalescing turning point and simple pole in the complex plane. The new asymptotic approximations are then analytically continued around infinity, to derive a uniform asymptotic approximation between the characteristic exponent v and the parameters a and q. Error bounds are either included or available for all approximations.

6 citations

01 Jan 1973
TL;DR: In this article, it is shown that for f bounded, locally integrable and positive, it is known that a unique positive solution u of (i.i.I) exists and this solution has been studied in various asymptotic limits.
Abstract: Here ¢ > 0 is a constant and f is a given function. Some background and references related to this physical problem are given in [4]° For f bounded, locally integrable and positive, it is known that a unique positive solution u of (i.I) exists° This solution has been studied in various asymptotic limits [3], [4], [6]° Of particular interest here are the limits t ~ for s fixed and ¢ ~ 0 for all t ~ O. We shall discuss both of these cases.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526