Real functions Riemann and related integrals Concept
Cauchy principal value
Summary
The Cauchy principal value gives a value to some improper integrals that do not converge in the usual sense, see the definition. It removes a symmetric neighborhood of the singular point, or integrates over a symmetric interval , and then takes the limit.
Where this leads
14 pages build on this one.
- Exponential integral
- Finite Hilbert transform
- Prandtl's lifting-line equation
- Singular integral equation
- Sokhotski–Plemelj formulae
- Conjugate function
- Logarithmic integral
- Hilbert transform
- Hadamard finite part
- Carleman's singular integral equation
- Riesz transform
- Airfoil equation
- Hypersingular integral equation
- Hilbert transform of sinusoids
Further reading
- Web https://en.wikipedia.org/wiki/Cauchy_principal_value, lead section
About this page
| Tag | 0SYR10HD4R |
|---|---|
| URI | m2://0SYR10HD4R |
| Aliases | principal-value-integral |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A42 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Exponential integral
- Finite Hilbert transform
- Prandtl's lifting-line equation
- Singular integral equation
- Sokhotski–Plemelj formulae
- Conjugate function
- Logarithmic integral
- Hilbert transform
- Hadamard finite part
- Carleman's singular integral equation
- Riesz transform
- Airfoil equation
- Hypersingular integral equation
- Hilbert transform of sinusoids