Cauchy Principal Value
Consider the difference in values of two limits:
The former is the Cauchy principal value of the otherwise ill-defined expression
Similarly, we have
but
The former is the principal value of the otherwise ill-defined expression
All of the above limits are cases of the indeterminate form ∞ − ∞.
These pathologies do not affect "Lebesgue-integrable" functions, that is, functions the integrals of whose absolute values are finite.
Read more about this topic: Improper Integral
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