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26 lines
1.0 KiB
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26 lines
1.0 KiB
Markdown
---
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title: Cauchy Principal Value
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tags:
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- math
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- real-analysis
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---
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# Notation
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$$
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\text{p.v.} \int_{-\infty}^{\infty} f(x)dx = \lim_{a\rightarrow+\infty} \int_{-a}^{a} f(x) dx = \lim_{a\rightarrow+\infty}[f(a) - f(-a)]
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$$
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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.
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# Reference
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* [_Real Analysis 64 | Cauchy Principal Value_. _www.youtube.com_, https://www.youtube.com/watch?v=0SP2b0nFpwI. Accessed 3 Jan. 2024.](https://www.youtube.com/watch?v=0SP2b0nFpwI)
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* [“Cauchy Principal Value.” _Wikipedia_, 31 Dec. 2023. _Wikipedia_, https://en.wikipedia.org/w/index.php?title=Cauchy_principal_value&oldid=1192842366.](https://en.wikipedia.org/wiki/Cauchy_principal_value) |