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Acta Mathematica Scientia 1999年第2期19卷 127-137页

作者：齐民友张果平 Department of Mathematics Wuhan University Wuhan 430072 China

In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.

关键词： asymptotic expansion degenerate critical point hypersurface distribution-valued meromorphic function analytic extension

asymptotic expansion of Some Sheffer Polynomials

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Journal of Mathematical Research and Exposition 2001年第4期21卷 513-524页

作者： C.B.Corcino Mindanan州立大学数学系

asymptotic expansion of two Sheffer polynomials, namely, Charlier and Laguerre, was obtained by L，C， Hsu6]using a combinatorial method， In this paper, L，C， Hsu's method in [6]has been put into a formal theorem that the author successfully applied to four other Sheffer polynomials: Poisson-Charlier, weighted Touchard, Toscano, and Angelescu polynomials， Within sonic specified domains remainder estimates have been obtained， Moreover, sonic spplicability and llimitation have been mentioned，

关键词： asymptotic expansion Sheffer polynomials

asymptotic expansion of Standardized χ^(p)(n) Distribution and Power Function of χ^(p)(n)-Test

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武汉大学学报:自然科学英文版 2023年第4期28卷 291-298页

作者： HU Hongchang HU Minbo School of Mathematics and Statistics Hubei Normal UniversityHuangshi 435002HubeiChina School of Mathematics and Statistics Yunnan UniversityKunming 650500YunnanChina

Suppose that Y follows a χ^(p)-distribution with n degrees of freedom, and Z is the standardized form of Y. Let f(z,n,p) and F(z,n,p) denote the density function and the distribution function of Z, respectively. In this paper, we obtain the asymptotic expansion for f(z,n,p) and F(z,n,p). The validity of these results is illuminated by some numerical examples. We also investigate the power function of χ^(p)-test by the asymptotic expansion.

关键词： P-norm distribution χ^(p)-distribution asymptotic expansion χ^(p)-test power function

asymptotic RESULTS FOR OVER-DISPERSED OPERATIONAL RISK BY USING THE asymptotic expansion METHOD

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Journal of Systems Science & Complexity 2014年第3期27卷 524-536页

作者： LU Zhaoyang School of Science Engineering University of Chinese Armed Police Forces

In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.

关键词： asymptotic expansion multivariate dependence operational risk over-dispersed valueat risk.

NOTE ON asymptotic expansion OF RIEMANN-SIEGEL INTEGRAL

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Analysis in Theory and Applications 2006年第2期22卷 120-135页

作者： Guangxiao Chen Zhongshan University China

In this note we establish two theorems concerning asymptotic expansion of Riemann-Siegel integrals as well as formula of generating function （double series） of coefficents of that expansion （for computation aims）; we also discuss similar results for Dirichlet series （L（s, fh） and L（s, X））, with m odd integer and X （ n ）（mod（ m ））（even） primitive characters （ inappendix B ） .

关键词： Rieraann-Siegel integral asymptotic expansion asymptotic functional equation Binet formula Titchmarsh technique

asymptotic expansion AND ESTIMATE OF THE LANDAU CONSTANT

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Analysis in Theory and Applications 2001年第4期17卷 58-64页

作者： A.Eisinberg G.Franzè N.Salerno DEIS Università della CalabriaItaly

Properties of Landau constant are investigated in this note. A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized. Moreover, we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.

关键词： asymptotic expansion hypergeometric function

asymptotic expansion OF THE MULTIVARIATE BERNSTEIN POLYNOMIALS ON A SIMPLEX

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Analysis in Theory and Applications 2000年第3期16卷 85-93页

作者： Abel Ulrich[]1 Ivan Mircea Fachhochschule Giessen-Firedbery University of Applied Sciences Fachbereich MNDWilhelm-Leuschner-Strasse 1361169 FriedbergGermany Department of Mathematics Technical University of Cluj-NapocaStr.C.Daicoviciu 153400 Cluj-NapocaRomania

In this note we study the local behaviour of the multi-variate Bernstein polynomials B, on the d-dimensional simplex S?R d. For function f admitting derivatives of sufficient high order in x∈S we derive the complete asymptotic expansion of Bnf as n tends to infinity. All the coefficients of n?1 that only depend on f and x are calculated explicitly. It turns out that combinatorial numbers play an important role. Par result generalize recent formulae due to R. Zhang in a way.

关键词： asymptotic expansion asymptotic Approximation Bernstein Polynomial asymptotic Relation Positive Linear Operator

asymptotic Energy expansion for Rational Power Polynomial Potentials

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Communications in Theoretical Physics 2012年第11期58卷 645-648页

作者： Asiri Nanayakkara Institute of Fundamental Studies Hanthana Road KandySri Lanka

asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form rig, mN are positive integers while coefficients bk ∈ C. As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of F functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.

关键词： asymptotic expansion eigen energies semiclassical

asymptotic Behavior of Singular Solution to the k-Hessian Equation with a Matukuma-Type Source

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Wuhan University Journal of Natural Sciences 2024年第3期29卷 242-256页

作者： LIU Jinyu WANG Biao CHANG Caihong College of Science Xi'an University of Science and TechnologyXi'an 710054ShaanxiChina

This paper is concerned with radially positive solutions of the k-Hessian equation involving a Matukuma-type source S_(k)(D^(2)(-φ))=|x|^(λ-2)/(1+|x|^(2))^(λ2)φ^(q),x∈Ω,where S_(k)(D^(2)(-φ))is the k-Hessian operator,q>k>1,λ>0,n>2k,k∈N,andΩis a suitable bounded do-main in R~*** turns out that there are two different types of radially positive solutions for k>1,i.e.,M-solution(singular at r=0)and Esolution(regular at r=0),which is distinct from the case when k=*** 1asymptotic expansions of M-solution step by step to the desired *** contrast to the case k=1,we require a more precise range of parameters due to repeated application of Taylor expansions,which also makes asymptotic expansions need more delicate investigation.

关键词： k-Hessian equation singular solutions asymptotic expansion

asymptotic expansions in the central limit theorem for a branching Wiener process

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Science China Mathematics 2021年第12期64卷 2759-2774页

作者： Zhi-Qiang Gao Quansheng Liu Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China LMBA Campus de TohannicUniversite de Bretagne-SudCNRS UMR 6205Vannes F-56000France

We consider a branching Wiener process in R^(d),in which particles reproduce as a super-critical Galton-Watson process and disperse according to a Wiener *** B⊂R^(d),let Z_(n)(B) be the number of particles of generation n located in *** study of the central limit theorem and related results about the counting measure Z_(n)(·)is important because such results give good descriptions of the con guration of the branching Wiener process at time *** earlier works,the exact convergence rate in the central limit theorem and the asymptotic expansion until the third order have been ***,we establish the asymptotic expansion of any order in the central limit theorem under a moment condition of the form EX(logX)^(1+λ)<∞.

关键词： branching Wiener process asymptotic expansion central limit theorem