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Cauchy Principle Value
Definition: Suppose we have a limit of the form lim_(as a goes to infinity)int_(-a to a)[f(x)dx] or lim_(as r goes to 0)[int_(a to c-r)[f(x)dx] + int_(c+r to b)[f(x)dx]] where f has a singularity point c on the interval (a,b). If a limit is one of these forms and it exists, then we say the Cauchy Principle Value of the improper integral exists
Source: Foundations of Analysis by Joseph L. Taylor, version 2.3