Luigi Gatteschi's work on asymptotics of special functions and their zeros
type: Item
instance of: scholarly article
title: Luigi Gatteschi's work on asymptotics of special functions and their zeros
zbMATH Open document ID: 1170.26007
author: Walter Gautschi
author: C. Giordano
published in: Numerical Algorithms
publication date: 2009-04-29T00:00:00Z
review text: In the present article, L. Gatteschi's work on asymptotics of special functions (Jacobi, Laguerre, Hermite polynomials; Bessel functions of the first and second kind; Airy functions; confluent hypergeometric functions etc.) and their zeros is reviewed ``along methodological lines''. Many papers of L. Gatteschi (1923--2007) appeared in Italian journals and are sometimes difficult to obtain, so that the work of the present authors is beneficial in many ways. Major tools appearing in Gatteschi's work are the quantitative use of a method of Tricomi for deriving the asymptotics of zeros of functions from the asymptotics of the functions themselves (with explicit error bounds), Van der Corput's theory of ``enveloping series'', methods based on linear second-order differential equations and uniform expansions. The survey puts Gatteschi's work very well in the historical context of the development of the field of asymptotics of special functions, it highlights Gatteschi's major results and ends with an extensive bibliographic list.
reviewed by: Thomas Stoll
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C15
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 5549492
zbMATH Keywords: Luigi Gatteschi's work
zbMATH Keywords: asymptotics
zbMATH Keywords: special functions
zbMATH Keywords: zeros
describes a project that uses: BIJ
MaRDI profile type: Publication
full work available at URL: s11075-008-9208-5
OpenAlex ID: W1985305079
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DOI: 10.1007/S11075-008-9208-5
description: scientific article; zbMATH DE number 5549492