A convergent version of Watson's lemma for double integrals

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2022-07-22 DOI:10.1080/10652469.2022.2098955

Chelo Ferreira, J. López, Ester Pérez Sinusía

引用次数: 0

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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沃森二重积分引理的收敛版

摘要【Nielsen，1906】对拉普拉斯变换的Watson引理进行了修改，导出了一个新的大的渐近展开式，并具有收敛的额外性质。在这一思想的启发下，本文推导了二维拉普拉斯变换的渐近展开式，适用于大变换和收敛变换。的展开式伴随着误差边界。举例说明了一些特殊函数的渐近展开式和收敛展开式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： 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.