Cauchy principal value [SEP] named after
Cauchy principal value
In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.
Formulation.
Depending on the type of singularity in the integrand "f", the Cauchy principal value is defined according to the following rules:
In some cases it is necessary to deal simultaneously with singularities both at a finite number "b" and at infinity. This is usually done by a limit of the form
The Cauchy
Cauchy theorem
Several theorems are named after Augustin-Louis Cauchy. Cauchy theorem may mean:
- Cauchy's integral theorem in complex analysis, also Cauchy's integral formula
- Cauchy's mean value theorem in real analysis, an extended form of the mean value theorem
- Cauchy's theorem (group theory)
- Cauchy's theorem (geometry) on rigidity of convex polytopes
- The Cauchy–Kovalevskaya theorem concerning partial differential equations
- The Cauchy–Peano theorem in the study of ordinary differential equations