A Generalization of the Method of Steepest Descent,
Abstract
The authors consider the asymptotic expansion as lambda approaches infinity of contour integrals with integrand H(lambda w(z)) g(z), H(t) being an entire function of t. When H is the exponential function, the asymptotic expansion of such an integral can be obtained by the method of steepest descent. The generalization of that method has two major new features. Firstly, the zeros of w(z) are critical points of the integrand. Secondly, there exist points from which no path of descent can be drawn; i.e., there exist curves which are boundaries between two hills of H(lambda w(z)). These features lead to new types of expansions for which the Mellin transform technique of Handelsman and Lew is ideally suited. The authors develop the general method and treat specific examples in detail. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1971
- Accession Number
- AD0732324
Entities
People
- Norman Bleistein
- Richard A. Handelsman
Organizations
- Denver Research Institute