Divergent Integral

divergent integral

[də′vər·jənt ′in·tə·grəl]
An improper integral which does not have a finite value.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Divergent Integral


an integral that has infinite limits of integration or an unbounded integrand and is either infinite or lacks a definite finite value. For example, the integral

defined as

diverges, since

On the other hand, the integral

diverges because

does not exist.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The technique of neglecting appropriately defined infinite quantities was devised by Hadamard, and the resulting finite value extracted from a divergent integral is referred to as the Hadamard finite part.
Application of this method with the method of regularization of divergent integrals [1] allowed to solve a number of problems for the lamellar shells with defects, such as [3 ...
Paycha seeks to clarify some aspects of regularization techniques, which are used to make sense of divergent integrals, discrete sums, or traces.