Principal part
From Wikipedia, the free encyclopedia
- This article is about the mathematical meaning. For the grammar term (a list of verb forms), see Principal parts.
In mathematics, the principal part has several independent meanings.
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[edit] Laurent series
principal part of the Laurent series of a function f(z),
is the series of terms with negative degree, that is
If f(z) has an essential singularity at p, then the principal part is an infinite sum, and vice versa.
[edit] Calculus
Consider the difference between the function differential and the actual increment:
The differential dy is the principal (linear) part of the function increment Δy.
[edit] Distribution theory
The term principal part is used for certain kinds of distribution having a singular support at a single point.
