wanweipedia

Principal part Redirected from 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 Δy.

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". Retrieved 31 March 2016.

External links


This page was last updated at 2021-01-25 18:35, update this pageView original page

All information on this site, including but not limited to text, pictures, etc., are reproduced on Wikipedia (wikipedia.org), following the . Creative Commons Attribution-ShareAlike License


Top

If the math, chemistry, physics and other formulas on this page are not displayed correctly, please useFirefox or Safari