# 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.

### Other articles related to "cauchy principal value, principal value, cauchy":

Improper Integral - Cauchy Principal Value
... Consider the difference in values of two limits The former is the Cauchy principal value of the otherwise ill-defined expression Similarly, we have but The former is the principal value of the ...
Cauchy Elastic Material - Isotropic Cauchy-elastic Materials
... For an isotropic material the Cauchy stress tensor can be expressed as a function of the left Cauchy-Green tensor ...
Cauchy Principal Value - Nomenclature
... The Cauchy principal value of a function can take on several nomenclatures, varying for different authors ...
Cauchy-continuous Function - Generalisations
... Cauchy continuity makes sense in situations more general than metric spaces, but then one must move from sequences to nets (or equivalently filters) ... The definition above applies, as long as the Cauchy sequence (x1, x2, …) is replaced with an arbitrary Cauchy net ... Equivalently, a function f is Cauchy-continuous if and only if, given any Cauchy filter F on X, then f(F) is a Cauchy filter on Y ...
Cauchy-continuous Function
... In mathematics, a Cauchy-continuous, or Cauchy-regular, function is a special kind of continuous function between metric spaces (or more general spaces) ... Cauchy-continuous functions have the useful property that they can always be (uniquely) extended to the Cauchy completion of their domain ...

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In our country today, very few children are raised to believe that their principal destiny is to serve their family, their country, or God.
Benjamin Spock (b. 1903)