Principal part

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In mathematics, the principal part has several independent meanings, but usually refers to the negative-power portion of the Laurent series of a function.

Laurent series definition[edit]

The principal part at of a function

is the portion of the Laurent series consisting of terms with negative degree.[1] That is,

is the principal part of at . has an essential singularity at , if and only if the principal part is an infinite sum.

Other definitions[edit]

Calculus[edit]

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[edit]

The term principal part is also used for certain kinds of distributions having a singular support at a single point.

See also[edit]

References[edit]

  1. ^ "laurent". Retrieved 31 March 2016. 

External links[edit]