The origin of the method of steepest descent
type: Item
instance of: scholarly article
title: The origin of the method of steepest descent
zbMATH Open document ID: 0894.01006
author: S. S. Petrova
author: A. D. Solov'ev
published in: Historia Mathematica
publication date: 1998-08-25T00:00:00Z
review text: A powerful method to estimate complex integrals of the form \(\int_C e^{nu(z)}g(z)dz\) (\(C\) is the contour of integration and \(u\), \(g\) are analytic functions) for large \(n\) is the so-called method of steepest descent or saddle-point method. The article under review offers a historical analysis of the creation of this method. The authors describe in detail the contributions of Laplace, Cauchy, Riemann and Debye, with particular attention to the work of Pavel Alexeevich Nekrasov (1853-1924).
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 41-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 1121602
zbMATH Keywords: P. A. Nekrasov
zbMATH Keywords: asymptotic estimate of integrals
zbMATH Keywords: saddle-point method
reviewed by: Michael von Renteln
MaRDI profile type: Publication
full work available at URL: hmat.1996.2146
OpenAlex ID: W1998271442
cites work: Q5736202
cites work: Q5732796
cites work: Q3250680
cites work: Q3232759
cites work: Q3329425
cites work: Q4074972
DOI: 10.1006/HMAT.1996.2146
description: scientific article; zbMATH DE number 1121602