{"title":"A convergent version of Watson's lemma for double integrals","authors":"Chelo Ferreira, J. López, Ester Pérez Sinusía","doi":"10.1080/10652469.2022.2098955","DOIUrl":null,"url":null,"abstract":"ABSTRACT A modification of Watson's lemma for Laplace transforms was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms for large and that are also convergent. The expansions of are accompanied by error bounds. Asymptotic and convergent expansions of some special functions are given as illustration.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"196 - 210"},"PeriodicalIF":0.7000,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2022.2098955","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
ABSTRACT A modification of Watson's lemma for Laplace transforms was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms for large and that are also convergent. The expansions of are accompanied by error bounds. Asymptotic and convergent expansions of some special functions are given as illustration.
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Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.
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