In mathematics, the principal part has several independent meanings, but usually refers to the negative-power portion of the Laurent series of a function.
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Laurent series definition
The principal part at
is the portion of the Laurent series consisting of terms with negative degree. That is,
is the principal part of
Calculus
Consider the difference between the function differential and the actual increment:
The differential dy is sometimes called the principal (linear) part of the function increment Δy.
Distribution theory
The term principal part is also used for certain kinds of distributions having a singular support at a single point.