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Asymptotic approximations
, 1994
"... I have been doing what I guess you won’t let me do when we are married, sitting up till 3 o’clock in the morning fighting hard against a mathematical difficulty. — Sir George Gabriel Stokes, from a letter to a young lady, March 19, 1857. Are you one of those tennisshoed liberals who wants to regula ..."
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I have been doing what I guess you won’t let me do when we are married, sitting up till 3 o’clock in the morning fighting hard against a mathematical difficulty. — Sir George Gabriel Stokes, from a letter to a young lady, March 19, 1857. Are you one of those tennisshoed liberals who wants to regulate everything? Let them grow any way they want. — Lucio Tavernini, email regarding the talk title, February 24, 1994.
ASYMPTOTIC APPROXIMATIONS FOR ELLIPTIC INTEGRALS
, 1993
"... Dedicated to Dick Askey and Frank Olver in gratitude for many years of friendship. Abstract. Symmetric elliptic integrals, which have been used as replacements for Legendre’s integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of th ..."
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of the variables are much larger than the others, asymptotic approximations with error bounds are presented. In most cases they are derived from a uniform approximation to the integrand. As an application the symmetric elliptic integrals of the first, second, and third kinds are proved to be linearly independent
Asymptotic Approximations in Quantum Calculus
, 2005
"... This paper aims to study the asymptotic approximation of some functions defined by the qJackson integrals, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical methods by giving their qanalogues. In particular, a qanalogue of the Watson’s lemma is discussed and new asym ..."
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This paper aims to study the asymptotic approximation of some functions defined by the qJackson integrals, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical methods by giving their qanalogues. In particular, a qanalogue of the Watson’s lemma is discussed and new
Asymptotic approximation of convex curves
 Arch. Math
, 1994
"... Abstract. L. Fejes Tóth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae are ext ..."
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Cited by 13 (3 self)
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Abstract. L. Fejes Tóth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae
On asymptotic approximation of the residual currents
"... We use a Dmodule approach to discuss positive examples for the existence of the unrestricted limit of the integrals involved in the approximation to the ColeffHerrera residual currents (in the complete intersection case.) Our results provide also asymptotic developments for these integrals. ..."
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Cited by 2 (2 self)
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We use a Dmodule approach to discuss positive examples for the existence of the unrestricted limit of the integrals involved in the approximation to the ColeffHerrera residual currents (in the complete intersection case.) Our results provide also asymptotic developments for these integrals.
Asymptotic approximations of orthogonal polynomials
"... It is well known that some orthogonal polynomials can be expressed in terms of Hermite polynomials taking limits in some of the parameters. Two of the most remarkable examples are the limit relations between the Jacobi and Laguerre polynomials and the Hermite polynomials. In this paper, we advance ..."
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ones. In this paper we express the asymptotic representation of the Charlier polynomials in terms of Hermite polynomials and show some numerical experiments about the approximation convergence.
ASYMPTOTIC APPROXIMATIONS OF INTEGRAL MANIFOLDS*
"... Abstract Multidegree of freedom nonlinear differential equations can often be transformed by means ofthe method ofaveraging into equivalent systems with only highorder terms. Under appropriate smallorder perturbation conditions these systems have unique surfaces of solutions called integral manifo ..."
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manifolds. They generalize the notions of periodic and almost periodic solutions for single degree of freedom systems. In parametric form the integral manifolds satisfy a certain system of partial differential ectuations. Conversely, an Nthorder asymptotic integral manifold is defined as a formal solution
Asymptotic Approximation Power for Neural Networks
"... This paper studies the asymptotic approximation power of radial basis function neural networks in the sup norm. The methods used are constructive and based on discretization of approximate identities. The effect of the kernel on the approximation order is discussed. 1 Introduction The purpose of t ..."
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This paper studies the asymptotic approximation power of radial basis function neural networks in the sup norm. The methods used are constructive and based on discretization of approximate identities. The effect of the kernel on the approximation order is discussed. 1 Introduction The purpose
ASYMPTOTIC APPROXIMATION OF EIGENVALUES OF VECTOR EQUATIONS
"... Abstract. A vectorial extension of the KellerRubinow method of computing asymptotic approximations of eigenvalues in bounded domains is presented. The method is applied to the problem of a multimode stepprofile cylindrical optical fibre, including the effects of polarisation. A comparison of the ..."
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Abstract. A vectorial extension of the KellerRubinow method of computing asymptotic approximations of eigenvalues in bounded domains is presented. The method is applied to the problem of a multimode stepprofile cylindrical optical fibre, including the effects of polarisation. A compar
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