The origin of the method of steepest descent
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).
scientific article; zbMATH DE number 1121602