Free-radical halogenation

29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church. 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 $z=a$ of a function

$f(z)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}{a}_k(z-a{)}^k$

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

$\sum _{k=-\mathrm{\infty }}^{-1}{a}_k(z-a{)}^k$

is the principal part of $f$ at $a$. $f(z)$ has an essential singularity at $a$, if and only if the principal part is an infinite sum.

Other definitions

Calculus

Consider the difference between the function differentialTemplate:Disambiguation needed and the actual increment:

$\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=f^{\prime }(x)+\epsilon$

$\mathrm{\Delta }y=f^{\prime }(x)\mathrm{\Delta }x+\epsilon \mathrm{\Delta }x=dy+\epsilon \mathrm{\Delta }x$

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

• Mittag-Leffler's theorem

• Cauchy principal value

External links

• Cauchy Principal Part at PlanetMath

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