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Uniform Asymptotic Expansions.
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The article was published on 1991-01-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Asymptotic analysis & Taylor expansions for the moments of functions of random variables.read more
Citations
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Journal Article
Numerical and asymptotic aspects of parabolic cylinder functions
TL;DR: Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered in this paper, one group in terms of elementary functions, another group based on Airy functions, and numerical tests are given for three expansions.
Uniform asymptotic expansion of integrals : a selection of problems
TL;DR: This paper discusses several “standard” problems and examples, in which known special functions are needed to construct uniform approximations, and discusses the recent interest and new insights in the Stokes phenomenon.
Book ChapterDOI
Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects
TL;DR: In this article, an ab initio frequency domain model of circular micro-resonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides, is discussed.
Dissertation
High-precision computation of uniform asymptotic expansions for special functions
TL;DR: New methods to obtain uniform asymptotic expansions for the numerical evaluation of special functions to high-precision are investigated, obtaining efficient new convergent and uniform expansions for numerically evaluating the confluent hypergeometric functions and the Lerch transcendent at high- Precision.
Journal ArticleDOI
An analysis of the impact of t. m. cherry's work on asymptotic expansions
TL;DR: Cherry's work on uniform asymptotic formulae for transition points in ordinary differential equations is probably his best known and most widely quoted piece of research as discussed by the authors. But it is not the most widely cited piece of work in this field.
References
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Journal Article
Numerical and asymptotic aspects of parabolic cylinder functions
TL;DR: Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered in this paper, one group in terms of elementary functions, another group based on Airy functions, and numerical tests are given for three expansions.
Journal ArticleDOI
Uniform asymptotic expansions of integrals: a selection of problems
TL;DR: A selection of uniform asymptotic methods for integrals, in particular on uniform approximations, can be found in this article, together with references to recent papers on the Stokes phenomenon.
Book ChapterDOI
Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects
TL;DR: In this article, an ab initio frequency domain model of circular micro-resonators, built on the physical notions that commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity with the modes supported by the straight bus waveguides, is discussed.
Dissertation
High-precision computation of uniform asymptotic expansions for special functions
TL;DR: New methods to obtain uniform asymptotic expansions for the numerical evaluation of special functions to high-precision are investigated, obtaining efficient new convergent and uniform expansions for numerically evaluating the confluent hypergeometric functions and the Lerch transcendent at high- Precision.
Journal ArticleDOI
An analysis of the impact of t. m. cherry's work on asymptotic expansions
TL;DR: Cherry's work on uniform asymptotic formulae for transition points in ordinary differential equations is probably his best known and most widely quoted piece of research as discussed by the authors. But it is not the most widely cited piece of work in this field.