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| title | tags | ||
|---|---|---|---|
| Cauchy Principal Value |
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Notation
\text{p.v.} \int_{-\infty}^{\infty} f(x)dx = \lim_{a\rightarrow+\infty} \int_{-a}^{a} f(x) dx = \lim_{a\rightarrow+\infty}[f(a) - f(-a)]
the Cauchy principal value is the method for assigning values to certain improper integrals which would otherwise be undefined. In this method, a singularity on an integral interval is avoided by limiting the integral interval to the non singular domain.