Current trends in asymptotics: some problems and some solutions
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In this paper, the authors discuss five topics of current interest in asymptotic analysis: the use of probabilistic methods to estimate the growth of combinatorial sequences, asymPTotic methods in the theory of random walks, the estimation of solutions of difference equations, asmptotic expansions in generalized scales, and the computation by asymptonotic methods of distributions whose moments are known.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1991-06-26 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotology.read more
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Book
Asymptotic enumeration methods
TL;DR: In this article, the saddle point and large singularities of analytic functions are used for graphical enumeration, including implicit functions, recurrences, and combinations of methods, which are related to our work.
Journal ArticleDOI
Painleve´-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
TL;DR: In this paper, the recurrence coefficients of semi-classical orthogonal polynomials related to a weight function w such that w/w is a rational function were shown to be solutions of nonlinear differential equations with respect to a well-chosen parameter.
Book ChapterDOI
Freud's equations for orthogonal polynomials as discrete Painlevé equations
TL;DR: In this article, the orthogonal polynomials with respect to an exponential weight function w(x) = exp(P(x)) were considered and the related equations for the recurrence coefficients have been explored by many people, starting essentially with Laguerre [49], in order to study special continued fractions, recurrence relations, and various asymptotic expansions.
Journal ArticleDOI
The Distribution of heights of binary trees and other simple trees
TL;DR: The number of binary trees of fixed size and given height is estimated asymptotically near the peak of the distribution and a local limit theorem with convergence to a theta law is established.
Dissertation
Autour de l'évaluation numérique des fonctions D-finies
TL;DR: In this paper, the authors explore trois grandes directions, i.e., the majoration des coefficients des developpements en serie of fonctions D-finies, the mise en pratique de l'algorithme "bit burst" de Chudnovsky et.
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Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.