Cauchy Principal Value

Notation

$$\text{p.v.}{\int }_{-\infty }^{\infty }f(x)dx=\underset{a\to +\infty }{\lim }{\int }_{-a}^{a}f(x)dx=\underset{a\to +\infty }{\lim }[f(a)-f(-a)]$$

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.

Reference

• Real Analysis 64 | Cauchy Principal Value. www.youtube.com, https://www.youtube.com/watch?v=0SP2b0nFpwI. Accessed 3 Jan. 2024.
• “Cauchy Principal Value.” Wikipedia, 31 Dec. 2023. Wikipedia, https://en.wikipedia.org/w/index.php?title=Cauchy_principal_value&oldid=1192842366.