Principal Part
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Principal Part

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

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 . If the Laurent series has an inner radius of convergence of 0 , then has an essential singularity at , if and only if the principal part is an infinite sum. If the inner radius of convergence is not 0, then may be regular at despite the Laurent series having an infinite principal part.

Other definitions

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 ?y.

Distribution theory

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

See also

References

  1. ^ Laurent. 16 October 2016. ISBN 9781467210782. Retrieved 2016.

External links


  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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