Topic
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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TL;DR: In this article, the equivalence of randomisation and normal theory distributions of linear combinations was discussed and the asymptotic randomisation distributions of statistics used in analysis of variance and in a closely related problem which includes, in particular, the problem of m -rankings.
Abstract: In a previous paper [5] the equivalence of randomisation and normal theory distributions of linear combinations was discussed. In the present paper we discuss the asymptotic randomisation distributions of statistics used in analysis of variance and in a closely related problem which includes, in particular, the “problem of m -rankings“. Kruskal [4] has studied the first of these questions in the case where observations are replaced by ranks.
10 citations
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20 Jul 2006
10 citations
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TL;DR: In this article, the problem of deriving Green-type asymptotic solutions from differential equations of general form d2 y /dz2 = X(a2>, z)y, for large values of a2, is reformulated.
Abstract: The problem of deriving Green-type asymptotic solutions from differential equations of general form d2 y /dz2 = X(a2>, z)y , for large values of a2, is reformulated. Combination of this formulation with the method of Mellin transforms leads further to a particularly convenient procedure for finding asymptotic expansions valid in transitional regions, and general uniform expansions. The methods are illustrated by detailed calculations for modified Bessel functions.
9 citations
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TL;DR: In this article, the asymptotic behavior of the Whittaker functions Mκ, μ(z) and Wκ, ε for large modulus of the parameter κ is considered.
Abstract: . The asymptotic behavior of the Whittaker functions Mκ, μ(z) and Wκ, μ(z) for large modulus of the parameter κ is considered. Asymptotic expansions in descending powers of √ κ are derived. The κ-independent coefficients of these expansions can be calculated in a simply way making these approximations quite useful in practise. An explicit error bound for the expansion of Mκ, μ(z) is also obtained.
9 citations
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TL;DR: In this article, an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation was considered, and the authors considered an application to nonlinear nonlinear problems.
Abstract: We consider an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation.
9 citations