Singular Integrals and their Evaluation
Abstract
In this work, integrals with simple or multiple poles which are located on the path of integration are systematically treated. It is shown that with each such integral an infinite set of values can be associated. Since the Principal Value, introduced by Cauchy, plays a key role in the subject, a detailed discussion of this concept is included, and a variety of methods for its explicit evaluation are presented. Various Plemelj formulas are also derived. An important feature, that may well be novel in this context, is a delta-function interpretation of the associated integrands, and its subsequent implications. Examples, related to cases frequently met in applications, are treated in detail in several appendices.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 22, 1979
- Accession Number
- ADA065055
Entities
People
- Phillip B. Abraham
Organizations
- Naval Underwater Systems Center